115 results match your criteria Annals Of Statistics[Journal]


UNIFORMLY VALID POST-REGULARIZATION CONFIDENCE REGIONS FOR MANY FUNCTIONAL PARAMETERS IN Z-ESTIMATION FRAMEWORK.

Ann Stat 2018 Dec 11;46(6B):3643-3675. Epub 2018 Sep 11.

Department of Biostatistics, Columbia University, 722 West 168th St, Rm 633, New York, New York 10032, USA,

In this paper, we develop procedures to construct simultaneous confidence bands for potentially infinite-dimensional parameters after model selection for general moment condition models where is potentially much larger than the sample size of available data, . This allows us to cover settings with functional response data where each of the parameters is a function. The procedure is based on the construction of score functions that satisfy Neyman orthogonality condition approximately. Read More

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http://dx.doi.org/10.1214/17-AOS1671DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6449050PMC
December 2018
1 Read

FEATURE ELIMINATION IN KERNEL MACHINES IN MODERATELY HIGH DIMENSIONS.

Ann Stat 2019 Feb;47(1):497-526

The University of North Carolina at Chapel Hill.

We develop an approach for feature elimination in statistical learning with kernel machines, based on recursive elimination of features. We present theoretical properties of this method and show that it is uniformly consistent in finding the correct feature space under certain generalized assumptions. We present a few case studies to show that the assumptions are met in most practical situations and present simulation results to demonstrate performance of the proposed approach. Read More

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http://dx.doi.org/10.1214/18-AOS1696DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6294291PMC
February 2019

ESTIMATION OF A MONOTONE DENSITY IN -SAMPLE BIASED SAMPLING MODELS.

Ann Stat 2018 17;46(5):2125-2152. Epub 2018 Aug 17.

Department of Statistics, Chinese University of Hong Kong, Shatin, NT, Hong Kong Sar.

We study the nonparametric estimation of a decreasing density function in a general -sample biased sampling model with weight (or bias) functions for = 1, …, . The determination of the monotone maximum likelihood estimator and its asymptotic distribution, except for the case when = 1, has been long missing in the literature due to certain non-standard structures of the likelihood function, such as non-separability and a lack of strictly positive second order derivatives of the negative of the log-likelihood function. The existence, uniqueness, self-characterization, consistency of and its asymptotic distribution at a fixed point are established in this article. Read More

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http://dx.doi.org/10.1214/17-AOS1614DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6251412PMC

Consistency and convergence rate of phylogenetic inference via regularization.

Ann Stat 2018 Aug 27;46(4):1481-1512. Epub 2018 Jun 27.

Program in Computational Biology Fred Hutchinson Cancer Research Center.

It is common in phylogenetics to have some, perhaps partial, information about the overall evolutionary tree of a group of organisms and wish to find an evolutionary tree of a specific gene for those organisms. There may not be enough information in the gene sequences alone to accurately reconstruct the correct "gene tree." Although the gene tree may deviate from the "species tree" due to a variety of genetic processes, in the absence of evidence to the contrary it is parsimonious to assume that they agree. Read More

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http://dx.doi.org/10.1214/17-AOS1592DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6191858PMC

BALL DIVERGENCE: NONPARAMETRIC TWO SAMPLE TEST.

Ann Stat 2018 Jun;46(3):1109-1137

Sun Yat-sen University.

In this paper, we first introduce Ball Divergence, a novel measure of the difference between two probability measures in separable Banach spaces, and show that the Ball Divergence of two probability measures is zero if and only if these two probability measures are identical without any moment assumption. Using Ball Divergence, we present a metric rank test procedure to detect the equality of distribution measures underlying independent samples. It is therefore robust to outliers or heavy-tail data. Read More

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http://dx.doi.org/10.1214/17-AOS1579DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6192286PMC

HIGH DIMENSIONAL CENSORED QUANTILE REGRESSION.

Ann Stat 2018 Feb 22;46(1):308-343. Epub 2018 Feb 22.

Department of Statistics University of Michigan, Ann Arbor, MI 48109, USA.

Censored quantile regression (CQR) has emerged as a useful regression tool for survival analysis. Some commonly used CQR methods can be characterized by stochastic integral-based estimating equations in a sequential manner across quantile levels. In this paper, we analyze CQR in a high dimensional setting where the regression functions over a continuum of quantile levels are of interest. Read More

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http://dx.doi.org/10.1214/17-AOS1551DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6193274PMC
February 2018
1 Read

ASSESSING ROBUSTNESS OF CLASSIFICATION USING ANGULAR BREAKDOWN POINT.

Ann Stat 2018 Dec 11;46(6B):3362-3389. Epub 2018 Sep 11.

University of North Carolina at Chapel Hill, USA.

Robustness is a desirable property for many statistical techniques. As an important measure of robustness, breakdown point has been widely used for regression problems and many other settings. Despite the existing development, we observe that the standard breakdown point criterion is not directly applicable for many classification problems. Read More

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http://dx.doi.org/10.1214/17-AOS1661DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6168219PMC
December 2018
1 Read

Optimal Shrinkage of Eigenvalues in the Spiked Covariance Model.

Ann Stat 2018 Aug 27;46(4):1742-1778. Epub 2018 Jun 27.

Department of Statistics, Stanford University.

We show that in a common high-dimensional covariance model, the choice of loss function has a profound effect on optimal estimation. In an asymptotic framework based on the Spiked Covariance model and use of orthogonally invariant estimators, we show that optimal estimation of the population covariance matrix boils down to design of an optimal shrinker that acts elementwise on the sample eigenvalues. Indeed, to each loss function there corresponds a unique admissible eigenvalue shrinker * dominating all other shrinkers. Read More

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https://projecteuclid.org/euclid.aos/1530086432
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http://dx.doi.org/10.1214/17-AOS1601DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6152949PMC
August 2018
18 Reads

A NEW PERSPECTIVE ON ROBUST -ESTIMATION: FINITE SAMPLE THEORY AND APPLICATIONS TO DEPENDENCE-ADJUSTED MULTIPLE TESTING.

Ann Stat 2018 Oct 17;46(5):1904-1931. Epub 2018 Aug 17.

Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544, USA.

Heavy-tailed errors impair the accuracy of the least squares estimate, which can be spoiled by a single grossly outlying observation. As argued in the seminal work of Peter Huber in 1973 [ (1973) 799-821], robust alternatives to the method of least squares are sorely needed. To achieve robustness against heavy-tailed sampling distributions, we revisit the Huber estimator from a new perspective by letting the tuning parameter involved diverge with the sample size. Read More

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http://dx.doi.org/10.1214/17-AOS1606DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6133288PMC
October 2018

LARGE COVARIANCE ESTIMATION THROUGH ELLIPTICAL FACTOR MODELS.

Ann Stat 2018 Aug 27;46(4):1383-1414. Epub 2018 Jun 27.

Dept of Operations Research & Financial Engineering, Sherrerd Hall, Princeton University, Princeton, NJ 08544, USA.

We propose a general Principal Orthogonal complEment Thresholding (POET) framework for large-scale covariance matrix estimation based on the approximate factor model. A set of high level sufficient conditions for the procedure to achieve optimal rates of convergence under different matrix norms is established to better understand how POET works. Such a framework allows us to recover existing results for sub-Gaussian data in a more transparent way that only depends on the concentration properties of the sample covariance matrix. Read More

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http://dx.doi.org/10.1214/17-AOS1588DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6133289PMC

DISTRIBUTED TESTING AND ESTIMATION UNDER SPARSE HIGH DIMENSIONAL MODELS.

Ann Stat 2018 Jun 3;46(3):1352-1382. Epub 2018 May 3.

Princeton University.

This paper studies hypothesis testing and parameter estimation in the context of the divide-and-conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various statistics from subsamples of size , where is the sample size. In both low dimensional and sparse high dimensional settings, we address the important question of how large can be, as grows large, such that the loss of efficiency due to the divide-and-conquer algorithm is negligible. Read More

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http://dx.doi.org/10.1214/17-AOS1587DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6051757PMC
June 2018
9 Reads

ARE DISCOVERIES SPURIOUS? DISTRIBUTIONS OF MAXIMUM SPURIOUS CORRELATIONS AND THEIR APPLICATIONS.

Ann Stat 2018 Jun 3;46(3):989-1017. Epub 2018 May 3.

Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544, USA.

Over the last two decades, many exciting variable selection methods have been developed for finding a small group of covariates that are associated with the response from a large pool. Can the discoveries by such data mining approaches be spurious due to high dimensionality and limited sample size? Can our fundamental assumptions on exogeneity of covariates needed for such variable selection be validated with the data? To answer these questions, we need to derive the distributions of the maximum spurious correlations given certain number of predictors, namely, the distribution of the correlation of a response variable with the best linear combinations of covariates , even when and are independent. When the covariance matrix of possesses the restricted eigenvalue property, we derive such distributions for both finite and diverging , using Gaussian approximation and empirical process techniques. Read More

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http://dx.doi.org/10.1214/17-AOS1575DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6014708PMC
June 2018
20 Reads

I-LAMM FOR SPARSE LEARNING: SIMULTANEOUS CONTROL OF ALGORITHMIC COMPLEXITY AND STATISTICAL ERROR.

Ann Stat 2018 Apr 3;46(2):814-841. Epub 2018 Apr 3.

Tencent AI Lab, Shennan Ave, Nanshan District, Shen Zhen, Guangdong, China.

We propose a computational framework named iterative local adaptive majorize-minimization (I-LAMM) to simultaneously control algorithmic complexity and statistical error when fitting high dimensional models. I-LAMM is a two-stage algorithmic implementation of the local linear approximation to a family of folded concave penalized quasi-likelihood. The first stage solves a convex program with a crude precision tolerance to obtain a coarse initial estimator, which is further refined in the second stage by iteratively solving a sequence of convex programs with smaller precision tolerances. Read More

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http://dx.doi.org/10.1214/17-AOS1568DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6007998PMC
April 2018
3 Reads

HIGH-DIMENSIONAL A-LEARNING FOR OPTIMAL DYNAMIC TREATMENT REGIMES.

Ann Stat 2018 Jun 3;46(3):925-957. Epub 2018 May 3.

Department of Statistics, North Carolina State University, Raleigh NC, U.S.A.

Precision medicine is a medical paradigm that focuses on finding the most effective treatment decision based on individual patient information. For many complex diseases, such as cancer, treatment decisions need to be tailored over time according to patients' responses to previous treatments. Such an adaptive strategy is referred as a dynamic treatment regime. Read More

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http://dx.doi.org/10.1214/17-AOS1570DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5966293PMC
June 2018
1 Read

Chernoff Index for Cox Test of Separate Parametric Families.

Ann Stat 2018 Feb 22;46(1):1-29. Epub 2018 Feb 22.

Department of Statistics, Columbia University, 1255 Amsterdam Avenue, New York, NY 10027.

The asymptotic efficiency of a generalized likelihood ratio test proposed by Cox is studied under the large deviations framework for error probabilities developed by Chernoff. In particular, two separate parametric families of hypotheses are considered (Cox, 1961, 1962). The significance level is set such that the maximal type I and type II error probabilities for the generalized likelihood ratio test decay exponentially fast with the same rate. Read More

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http://dx.doi.org/10.1214/16-AOS1532DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5865707PMC
February 2018
1 Read

TARGETED SEQUENTIAL DESIGN FOR TARGETED LEARNING INFERENCE OF THE OPTIMAL TREATMENT RULE AND ITS MEAN REWARD.

Ann Stat 2017 15;45(6):2537-2564. Epub 2017 Dec 15.

University of California, Berkeley.

This article studies the targeted sequential inference of an optimal treatment rule (TR) and its mean reward in the non-exceptional case, , assuming that there is no stratum of the baseline covariates where treatment is neither beneficial nor harmful, and under a companion margin assumption. Our pivotal estimator, whose definition hinges on the targeted minimum loss estimation (TMLE) principle, actually infers the mean reward under the current estimate of the optimal TR. This data-adaptive statistical parameter is worthy of interest on its own. Read More

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http://dx.doi.org/10.1214/16-AOS1534DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5794253PMC
December 2017
1 Read

NONPARAMETRIC GOODNESS-OF-FIT TESTS FOR UNIFORM STOCHASTIC ORDERING.

Ann Stat 2017 15;45(6):2565-2589. Epub 2017 Dec 15.

Department of Statistics, University of South Carolina.

We propose distance-based goodness-of-fit (GOF) tests for uniform stochastic ordering with two continuous distributions and , both of which are unknown. Our tests are motivated by the fact that when and are uniformly stochastically ordered, the ordinal dominance curve = is star-shaped. We derive asymptotic distributions and prove that our testing procedure has a unique least favorable configuration of and for ∈ [1,∞]. Read More

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http://dx.doi.org/10.1214/16-AOS1535DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5771311PMC
December 2017
1 Read

TENSOR DECOMPOSITIONS AND SPARSE LOG-LINEAR MODELS.

Ann Stat 2017 21;45(1):1-38. Epub 2017 Feb 21.

Duke University.

Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. Read More

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http://dx.doi.org/10.1214/15-AOS1414DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5764221PMC
February 2017
1 Read

HIGHER ORDER ESTIMATING EQUATIONS FOR HIGH-DIMENSIONAL MODELS.

Ann Stat 2017 Oct 31;45(5):1951-1987. Epub 2017 Oct 31.

Harvard University and Universiteit Leiden.

We introduce a new method of estimation of parameters in semi-parametric and nonparametric models. The method is based on estimating equations that are -statistics in the observations. The -statistics are based on higher order influence functions that extend ordinary linear influence functions of the parameter of interest, and represent higher derivatives of this parameter. Read More

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https://projecteuclid.org/euclid.aos/1509436824
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http://dx.doi.org/10.1214/16-AOS1515DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6453538PMC
October 2017
3 Reads

CAUSAL INFERENCE WITH A GRAPHICAL HIERARCHY OF INTERVENTIONS.

Ann Stat 2016 Dec 23;44(6):2433-2466. Epub 2016 Nov 23.

School of Public Health, Harvard University, 677 Huntington Avenue, Kresge Building, Boston, Massachusetts 02115,

Identifying causal parameters from observational data is fraught with subtleties due to the issues of selection bias and confounding. In addition, more complex questions of interest, such as effects of treatment on the treated and mediated effects may not always be identified even in data where treatment assignment is known and under investigator control, or may be identified under one causal model but not another. Increasingly complex effects of interest, coupled with a diversity of causal models in use resulted in a fragmented view of identification. Read More

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http://dx.doi.org/10.1214/15-AOS1411DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5597261PMC
December 2016
1 Read

Asymptotics of empirical eigenstructure for high dimensional spiked covariance.

Ann Stat 2017 Jun 13;45(3):1342-1374. Epub 2017 Jun 13.

Princeton University.

We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the magnitude of spiked eigenvalues, sample size, and dimensionality. This regime allows high dimensionality and diverging eigenvalues and provides new insights into the roles that the leading eigenvalues, sample size, and dimensionality play in principal component analysis. Our results are a natural extension of those in Paul (2007) to a more general setting and solve the rates of convergence problems in Shen et al. Read More

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http://dx.doi.org/10.1214/16-AOS1487DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5563862PMC
June 2017
6 Reads

MIMICKING COUNTERFACTUAL OUTCOMES TO ESTIMATE CAUSAL EFFECTS.

Authors:
Judith J Lok

Ann Stat 2017 Apr 16;45(2):461-499. Epub 2017 May 16.

Department of Biostatistics, Harvard School of Public Health.

In observational studies, treatment may be adapted to covariates at several times without a fixed protocol, in continuous time. Treatment influences covariates, which influence treatment, which influences covariates, and so on. Then even time-dependent Cox-models cannot be used to estimate the net treatment effect. Read More

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http://dx.doi.org/10.1214/15-AOS1433DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5531214PMC

MODELING DEPENDENT GENE EXPRESSION.

Ann Stat 2012 11;6(2):542-560. Epub 2012 Jun 11.

University of Texas, M.D. Anderson Cancer Center, Department of Gynecologic Oncology, Houston, Texas 7030, USA.

In this paper we propose a Bayesian approach for inference about dependence of high throughput gene expression. Our goals are to use prior knowledge about pathways to anchor inference about dependence among genes; to account for this dependence while making inferences about differences in mean expression across phenotypes; and to explore differences in the dependence itself across phenotypes. Useful features of the proposed approach are a model-based parsimonious representation of expression as an ordinal outcome, a novel and flexible representation of prior information on the nature of dependencies, and the use of a coherent probability model over both the structure and strength of the dependencies of interest. Read More

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http://dx.doi.org/10.1214/11-AOAS525DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5412732PMC
June 2012
7 Reads

A PARTIALLY LINEAR FRAMEWORK FOR MASSIVE HETEROGENEOUS DATA.

Ann Stat 2016 Aug 7;44(4):1400-1437. Epub 2016 Jul 7.

Department of operations research, and financial engineering, Princeton University, Princeton, New Jersey 08544, USA.

We consider a partially linear framework for modelling massive heterogeneous data. The major goal is to extract common features across all sub-populations while exploring heterogeneity of each sub-population. In particular, we propose an aggregation type estimator for the commonality parameter that possesses the (non-asymptotic) minimax optimal bound and asymptotic distribution as if there were no heterogeneity. Read More

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http://dx.doi.org/10.1214/15-AOS1410DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5394596PMC
August 2016
9 Reads

Optimal designs for comparing curves.

Ann Stat 2016 Jun 11;44(3):1103-1130. Epub 2016 Apr 11.

Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany.

We consider the optimal design problem for a comparison of two regression curves, which is used to establish the similarity between the dose response relationships of two groups. An optimal pair of designs minimizes the width of the confidence band for the difference between the two regression functions. Optimal design theory (equivalence theorems, efficiency bounds) is developed for this non standard design problem and for some commonly used dose response models optimal designs are found explicitly. Read More

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http://dx.doi.org/10.1214/15-AOS1399DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4914141PMC
June 2016
1 Read

Optimal designs in regression with correlated errors.

Ann Stat 2016 Feb 10;44(1):113-152. Epub 2015 Dec 10.

School of Mathematics, Cardiff University, Cardiff, CF24 4AG, UK.

This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class of regression models and covariance kernels. We propose a class of estimators which are only slightly more complicated than the ordinary least-squares estimators. Read More

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http://dx.doi.org/10.1214/15-AOS1361DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4914140PMC
February 2016
2 Reads

LOCAL INDEPENDENCE FEATURE SCREENING FOR NONPARAMETRIC AND SEMIPARAMETRIC MODELS BY MARGINAL EMPIRICAL LIKELIHOOD.

Ann Stat 2016;44(2):515-539. Epub 2016 Mar 17.

Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, North Carolina 27695-8203, USA,

We consider an independence feature screening technique for identifying explanatory variables that locally contribute to the response variable in high-dimensional regression analysis. Without requiring a specific parametric form of the underlying data model, our approach accommodates a wide spectrum of nonparametric and semiparametric model families. To detect the local contributions of explanatory variables, our approach constructs empirical likelihood locally in conjunction with marginal nonparametric regressions. Read More

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http://dx.doi.org/10.1214/15-AOS1374DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4883127PMC
March 2016
4 Reads
2.180 Impact Factor

SEMIPARAMETRIC EFFICIENT ESTIMATION FOR SHARED-FRAILTY MODELS WITH DOUBLY-CENSORED CLUSTERED DATA.

Ann Stat 2016 Jun 11;44(3):1298-1331. Epub 2016 Apr 11.

Department of Statistics, University of California, Davis, California, 95616, U.S.A.

In this paper, we investigate frailty models for clustered survival data that are subject to both left- and right-censoring, termed "doubly-censored data". This model extends current survival literature by broadening the application of frailty models from right-censoring to a more complicated situation with additional left censoring. Our approach is motivated by a recent Hepatitis B study where the sample consists of families. Read More

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http://projecteuclid.org/euclid.aos/1460381694
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http://dx.doi.org/10.1214/15-AOS1406DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5841260PMC
June 2016
3 Reads

GLOBAL SOLUTIONS TO FOLDED CONCAVE PENALIZED NONCONVEX LEARNING.

Ann Stat 2016 Apr;44(2):629-659

The Pennsylvania State University.

This paper is concerned with solving nonconvex learning problems with folded concave penalty. Despite that their global solutions entail desirable statistical properties, there lack optimization techniques that guarantee global optimality in a general setting. In this paper, we show that a class of nonconvex learning problems are equivalent to general quadratic programs. Read More

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http://dx.doi.org/10.1214/15-AOS1380DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4851172PMC
April 2016
20 Reads

OPTIMAL SHRINKAGE ESTIMATION OF MEAN PARAMETERS IN FAMILY OF DISTRIBUTIONS WITH QUADRATIC VARIANCE.

Ann Stat 2016 Mar 16;44(2):564-597. Epub 2016 Mar 16.

The Wharton School, University of Pennsylvania, Philadelphia, PA 19104,

This paper discusses the simultaneous inference of mean parameters in a family of distributions with quadratic variance function. We first introduce a class of semi-parametric/parametric shrinkage estimators and establish their asymptotic optimality properties. Two specific cases, the location-scale family and the natural exponential family with quadratic variance function, are then studied in detail. Read More

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http://dx.doi.org/10.1214/15-AOS1377DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4816092PMC
March 2016
1 Read

STATISTICAL INFERENCE FOR THE MEAN OUTCOME UNDER A POSSIBLY NON-UNIQUE OPTIMAL TREATMENT STRATEGY.

Ann Stat 2016 Apr 17;44(2):713-742. Epub 2016 Mar 17.

University of California, Berkeley.

We consider challenges that arise in the estimation of the mean outcome under an optimal individualized treatment strategy defined as the treatment rule that maximizes the population mean outcome, where the candidate treatment rules are restricted to depend on baseline covariates. We prove a necessary and sufficient condition for the pathwise differentiability of the optimal value, a key condition needed to develop a regular and asymptotically linear (RAL) estimator of the optimal value. The stated condition is slightly more general than the previous condition implied in the literature. Read More

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http://dx.doi.org/10.1214/15-AOS1384DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6338452PMC

Bayesian -optimal discriminating designs.

Ann Stat 2015 Oct;43(5):1959-1985

St. Petersburg State University, Department of Mathematics, St. Petersburg, Russia,

The problem of constructing Bayesian optimal discriminating designs for a class of regression models with respect to the -optimality criterion introduced by Atkinson and Fedorov (1975a) is considered. It is demonstrated that the discretization of the integral with respect to the prior distribution leads to locally -optimal discriminating design problems with a large number of model comparisons. Current methodology for the numerical construction of discrimination designs can only deal with a few comparisons, but the discretization of the Bayesian prior easily yields to discrimination design problems for more than 100 competing models. Read More

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http://dx.doi.org/10.1214/15-AOS1333DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4793413PMC
October 2015
7 Reads

ESTIMATION OF FUNCTIONALS OF SPARSE COVARIANCE MATRICES.

Ann Stat 2015;43(6):2706-2737

Department of Operations Research and Financial Engineering Princeton University Princeton, New Jersey 08544 USA.

High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other ℓ norms. Motivated by the computation of critical values of such tests, we investigate the difficulty of estimation the functionals of sparse correlation matrices. Specifically, we show that simple plug-in procedures based on thresholded estimators of correlation matrices are sparsity-adaptive and minimax optimal over a large class of correlation matrices. Read More

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http://dx.doi.org/10.1214/15-AOS1357DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4719663PMC
January 2015
2 Reads

PROJECTED PRINCIPAL COMPONENT ANALYSIS IN FACTOR MODELS.

Ann Stat 2016 Feb;44(1):219-254

Princeton University.

This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employees principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to high-dimensional factor analysis, the projection removes noise components. We show that the unobserved latent factors can be more accurately estimated than the conventional PCA if the projection is genuine, or more precisely, when the factor loading matrices are related to the projected linear space. Read More

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http://dx.doi.org/10.1214/15-AOS1364DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4714810PMC
February 2016
2 Reads

QUADRO: A SUPERVISED DIMENSION REDUCTION METHOD VIA RAYLEIGH QUOTIENT OPTIMIZATION.

Ann Stat 2015;43(4):1498-1534

Princeton University.

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method-named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization)-for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. Read More

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http://www.stat.uchicago.edu/~zke/files/AOS1307.pdf
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http://projecteuclid.org/euclid.aos/1434546213
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http://dx.doi.org/10.1214/14-AOS1307DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4712455PMC
January 2015
5 Reads

APPROXIMATION AND ESTIMATION OF -CONCAVE DENSITIES VIA RÉNYI DIVERGENCES.

Ann Stat 2016 11;44(3):1332-1359. Epub 2016 Apr 11.

University of Washington.

In this paper, we study the approximation and estimation of -concave densities via Rényi divergence. We first show that the approximation of a probability measure by an -concave density exists and is unique via the procedure of minimizing a divergence functional proposed by [ (2010) 2998-3027] if and only if admits full-dimensional support and a first moment. We also show continuity of the divergence functional in : if → in the Wasserstein metric, then the projected densities converge in weighted metrics and uniformly on closed subsets of the continuity set of the limit. Read More

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http://dx.doi.org/10.1214/15-AOS1408DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5619680PMC
April 2016
1 Read

GLOBAL RATES OF CONVERGENCE OF THE MLES OF LOG-CONCAVE AND -CONCAVE DENSITIES.

Ann Stat 2016 11;44(3):954-981. Epub 2016 Apr 11.

University of Minnesota and University of Washington.

We establish global rates of convergence for the Maximum Likelihood Estimators (MLEs) of log-concave and -concave densities on ℝ. The main finding is that the rate of convergence of the MLE in the Hellinger metric is no worse than when -1 < < ∞ where = 0 corresponds to the log-concave case. We also show that the MLE does not exist for the classes of -concave densities with < -1. Read More

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http://dx.doi.org/10.1214/15-AOS1394DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5619328PMC
April 2016
1 Read

ASYMPTOTICS FOR CHANGE-POINT MODELS UNDER VARYING DEGREES OF MIS-SPECIFICATION.

Ann Stat 2016 Feb 10;44(1):153-182. Epub 2015 Dec 10.

North Carolina State University, University of Michigan and University of North Carolina.

Change-point models are widely used by statisticians to model drastic changes in the pattern of observed data. Least squares/maximum likelihood based estimation of change-points leads to curious asymptotic phenomena. When the change-point model is correctly specified, such estimates generally converge at a fast rate () and are asymptotically described by minimizers of a jump process. Read More

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http://dx.doi.org/10.1214/15-AOS1362DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4678008PMC
February 2016
6 Reads

GLOBALLY ADAPTIVE QUANTILE REGRESSION WITH ULTRA-HIGH DIMENSIONAL DATA.

Ann Stat 2015 Oct;43(5):2225-2258

University of Michigan.

Quantile regression has become a valuable tool to analyze heterogeneous covaraite-response associations that are often encountered in practice. The development of quantile regression methodology for high dimensional covariates primarily focuses on examination of model sparsity at a single or multiple quantile levels, which are typically prespecified ad hoc by the users. The resulting models may be sensitive to the specific choices of the quantile levels, leading to difficulties in interpretation and erosion of confidence in the results. Read More

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http://dx.doi.org/10.1214/15-AOS1340DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4654965PMC
October 2015
2 Reads

EXACT MINIMAX ESTIMATION OF THE PREDICTIVE DENSITY IN SPARSE GAUSSIAN MODELS.

Ann Stat 2015;43(3):937-961

Department of Statistics, Sequoia Hall, 390 Serra Mall, Stanford University, Stanford, California 94305-4065, USA.

We consider estimating the predictive density under Kullback-Leibler loss in an sparse Gaussian sequence model. Explicit expressions of the first order minimax risk along with its exact constant, asymptotically least favorable priors and optimal predictive density estimates are derived. Compared to the sparse recovery results involving point estimation of the normal mean, new decision theoretic phenomena are seen. Read More

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http://dx.doi.org/10.1214/14-AOS1251DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4593074PMC
January 2015
2 Reads

Estimation and Inference in Generalized Additive Coefficient Models for Nonlinear Interactions with High-Dimensional Covariates.

Ann Stat 2015 Oct;43(5):2102-2131

University of California, Riverside.

In the low-dimensional case, the generalized additive coefficient model (GACM) proposed by Xue and Yang [ (2006) 1423-1446] has been demonstrated to be a powerful tool for studying nonlinear interaction effects of variables. In this paper, we propose estimation and inference procedures for the GACM when the dimension of the variables is high. Specifically, we propose a groupwise penalization based procedure to distinguish significant covariates for the "large small " setting. Read More

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http://www.stat.tamu.edu/~carroll/ftp/2014.papers.directory/
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http://projecteuclid.org/euclid.aos/1438606855
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http://dx.doi.org/10.1214/15-AOS1344DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4578655PMC
October 2015
1 Read

FUSED KERNEL-SPLINE SMOOTHING FOR REPEATEDLY MEASURED OUTCOMES IN A GENERALIZED PARTIALLY LINEAR MODEL WITH FUNCTIONAL SINGLE INDEX.

Ann Stat 2015;43(5):1929-1958

Harvard University, University of South Carolina, and Columbia University.

We propose a generalized partially linear functional single index risk score model for repeatedly measured outcomes where the index itself is a function of time. We fuse the nonparametric kernel method and regression spline method, and modify the generalized estimating equation to facilitate estimation and inference. We use local smoothing kernel to estimate the unspecified coefficient functions of time, and use B-splines to estimate the unspecified function of the single index component. Read More

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http://dx.doi.org/10.1214/15-AOS1330DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4536976PMC
January 2015
2 Reads

HYPOTHESIS TESTING FOR HIGH-DIMENSIONAL SPARSE BINARY REGRESSION.

Ann Stat 2015 Feb;43(1):352-381

Department of Biostatistics, Harvard University, 655 Huntington Avenue, SPH2, 4th Floor, Boston, Massachusetts 02115, USA.

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate the complexity of the hypothesis testing problem when the design matrix is sparse. We observe a new phenomenon in the behavior of detection boundary which does not occur in the case of Gaussian linear regression. Read More

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http://dx.doi.org/10.1214/14-AOS1279DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4522432PMC
February 2015
2 Reads

STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION.

Ann Stat 2014 Jun;42(3):819-849

Princeton University and University of Minnesota.

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. Read More

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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4295817PMC
June 2014
5 Reads

Endogeneity in High Dimensions.

Ann Stat 2014 Jun;42(3):872-917

Department of Mathematics, University of Maryland, College Park, MD 20742.

Most papers on high-dimensional statistics are based on the assumption that none of the regressors are correlated with the regression error, namely, they are exogenous. Yet, endogeneity can arise incidentally from a large pool of regressors in a high-dimensional regression. This causes the inconsistency of the penalized least-squares method and possible false scientific discoveries. Read More

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http://projecteuclid.org/euclid.aos/1400592646
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http://dx.doi.org/10.1214/13-AOS1202DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4286899PMC
June 2014
29 Reads

ADAPTIVE ROBUST VARIABLE SELECTION.

Ann Stat 2014 Feb;42(1):324-351

Princeton University, University of Southern California and IBM T.J. Watson Research Center.

Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with weighted -penalty, called weighted robust Lasso (WR-Lasso), in which weights are introduced to ameliorate the bias problem induced by the -penalty. In the ultra-high dimensional setting, where the dimensionality can grow exponentially with the sample size, we investigate the model selection oracle property and establish the asymptotic normality of the WR-Lasso. Read More

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http://dx.doi.org/10.1214/13-AOS1191DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4286898PMC
February 2014
4 Reads

A SIGNIFICANCE TEST FOR THE LASSO.

Ann Stat 2014 Apr;42(2):413-468

Department of Health, Research & Policy, Department of Statistics, Stanford University, Stanford, California 94305, USA.

In the sparse linear regression setting, we consider testing the significance of the predictor variable that enters the current lasso model, in the sequence of models visited along the lasso solution path. We propose a simple test statistic based on lasso fitted values, called the , and show that when the true model is linear, this statistic has an Exp(1) asymptotic distribution under the null hypothesis (the null being that all truly active variables are contained in the current lasso model). Our proof of this result for the special case of the first predictor to enter the model (i. Read More

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http://dx.doi.org/10.1214/13-AOS1175DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4285373PMC
April 2014
1 Read

OPTIMAL COMPUTATIONAL AND STATISTICAL RATES OF CONVERGENCE FOR SPARSE NONCONVEX LEARNING PROBLEMS.

Ann Stat 2014 ;42(6):2164-2201

Department of Statistics Rutgers University Piscataway, New Jersey 08854 USA

We provide theoretical analysis of the statistical and computational properties of penalized -estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this category, including least squares regression with nonconvex regularization, generalized linear models with nonconvex regularization and sparse elliptical random design regression. For these problems, it is intractable to calculate the global solution due to the nonconvex formulation. Read More

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http://dx.doi.org/10.1214/14-AOS1238DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276088PMC
January 2014
5 Reads

COVARIANCE ASSISTED SCREENING AND ESTIMATION.

Ann Stat 2014 Nov;42(6):2202-2242

Princeton University and Carnegie Mellon University.

Consider a linear model = β + , where = and ~ (0, ). The vector β is unknown and it is of interest to separate its nonzero coordinates from the zero ones (i.e. Read More

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http://projecteuclid.org/euclid.aos/1413810726
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http://dx.doi.org/10.1214/14-AOS1243DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4274608PMC
November 2014
3 Reads

LOCAL CASE-CONTROL SAMPLING: EFFICIENT SUBSAMPLING IN IMBALANCED DATA SETS.

Ann Stat 2014 Oct;42(5):1693-1724

Department of Statistics, Stanford University, 390 Serra Mall, Stanford, California 94305-4065, USA.

For classification problems with significant class imbalance, subsampling can reduce computational costs at the price of inflated variance in estimating model parameters. We propose a method for subsampling efficiently for logistic regression by adjusting the class balance locally in feature space via an accept-reject scheme. Our method generalizes standard case-control sampling, using a pilot estimate to preferentially select examples whose responses are conditionally rare given their features. Read More

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http://dx.doi.org/10.1214/14-AOS1220DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4258397PMC
October 2014