16 results match your criteria Bernoulli[Journal]

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Expected Number and Height Distribution of Critical Points of Smooth Isotropic Gaussian Random Fields.

Bernoulli (Andover) 2018 Nov 18;24(4B):3422-3446. Epub 2018 Apr 18.

University of California, San Diego.

We obtain formulae for the expected number and height distribution of critical points of smooth isotropic Gaussian random fields parameterized on Euclidean space or spheres of arbitrary dimension. The results hold in general in the sense that there are no restrictions on the covariance function of the field except for smoothness and isotropy. The results are based on a characterization of the distribution of the Hessian of the Gaussian field by means of the family of Gaussian orthogonally invariant (GOI) matrices, of which the Gaussian orthogonal ensemble (GOE) is a special case. Read More

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http://dx.doi.org/10.3150/17-BEJ964DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6738978PMC
November 2018

Stein's method and approximating the quantum harmonic oscillator.

Bernoulli (Andover) 2019 Feb 12;25(1):89-111. Epub 2018 Dec 12.

Université de Liège, Département de Mathématique, B37 12 allée de la découverte, B-4000 Liège.

Hall et al. (2014) recently proposed that quantum theory can be understood as the continuum limit of a deterministic theory in which there is a large, but finite, number of classical "worlds." A resulting Gaussian limit theorem for particle positions in the ground state, agreeing with quantum theory, was conjectured in Hall et al. Read More

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http://dx.doi.org/10.3150/17-BEJ960DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6550468PMC
February 2019
1 Read

Exponential bounds for the hypergeometric distribution.

Bernoulli (Andover) 2017 Aug 17;23(3):1911-1950. Epub 2017 Mar 17.

Department of Statistics, Box 354322, University of Washington, Seattle, WA 98195-4322, USA.

We establish exponential bounds for the hypergeometric distribution which include a finite sampling correction factor, but are otherwise analogous to bounds for the binomial distribution due to León and Perron ( (2003) 345-354) and Talagrand ( (1994) 28-76). We also extend a convex ordering of Kemperman's ( (1973) 149-164) for sampling without replacement from populations of real numbers between zero and one: a population of all zeros or ones (and hence yielding a hypergeometric distribution in the upper bound) gives the extreme case. Read More

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http://dx.doi.org/10.3150/15-BEJ800DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5839521PMC
August 2017
2 Reads

Statistical analysis of latent generalized correlation matrix estimation in transelliptical distribution.

Authors:
Fang Han Han Liu

Bernoulli (Andover) 2017 Feb 27;23(1):23-57. Epub 2016 Sep 27.

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

Correlation matrix plays a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). Read More

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http://dx.doi.org/10.3150/15-BEJ702DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5360110PMC
February 2017
4 Reads

Information bounds for Gaussian copulas.

Bernoulli (Andover) 2014 ;20(2):604-622

Professor of Statistics and Biostatistics University of Washington Seattle, WA 98195-4322.

Often of primary interest in the analysis of multivariate data are the copula parameters describing the dependence among the variables, rather than the univariate marginal distributions. Since the ranks of a multivariate dataset are invariant to changes in the univariate marginal distributions, rank-based estimators are natural candidates for semiparametric copula estimation. Asymptotic information bounds for such estimators can be obtained from an asymptotic analysis of the rank likelihood, i. Read More

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http://dx.doi.org/10.3150/12-BEJ499DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4193671PMC
January 2014
4 Reads

Asymptotics of nonparametric L-1 regression models with dependent data.

Bernoulli (Andover) 2014 Aug;20(3):1532-1559

Department of Statistics, Penn State University, University Park, PA 16802.

We investigate asymptotic properties of least-absolute-deviation or median quantile estimates of the location and scale functions in nonparametric regression models with dependent data from multiple subjects. Under a general dependence structure that allows for longitudinal data and some spatially correlated data, we establish uniform Bahadur representations for the proposed median quantile estimates. The obtained Bahadur representations provide deep insights into the asymptotic behavior of the estimates. Read More

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http://dx.doi.org/10.3150/13-BEJ532DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4060752PMC
August 2014
5 Reads

Theory of the Self-learning -Matrix.

Bernoulli (Andover) 2013 Nov;19(5A):1790-1817

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

Cognitive assessment is a growing area in psychological and educational measurement, where tests are given to assess mastery/deficiency of attributes or skills. A key issue is the correct identification of attributes associated with items in a test. In this paper, we set up a mathematical framework under which theoretical properties may be discussed. Read More

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http://projecteuclid.org/euclid.bj/1383661203
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http://dx.doi.org/10.3150/12-BEJ430DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4011940PMC
November 2013
9 Reads

Chernoff's density is log-concave.

Bernoulli (Andover) 2014 Feb;20(1):231-244

Department of Statistics, University of Washington, Seattle, WA 98195-4322, USA.

We show that the density of = argmax{ - }, sometimes known as Chernoff's density, is log-concave. We conjecture that Chernoff's density is strongly log-concave or "super-Gaussian", and provide evidence in support of the conjecture. Read More

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http://dx.doi.org/10.3150/12-BEJ483DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3993999PMC
February 2014
3 Reads

On the maximal size of large-average and ANOVA-fit submatrices in a Gaussian random matrix.

Bernoulli (Andover) 2013 ;19(1):275-294

Merck & Co., Inc., One Merck Drive, Whitehouse Station, NJ 08889, USA.

We investigate the maximal size of distinguished submatrices of a Gaussian random matrix. Of interest are submatrices whose entries have an average greater than or equal to a positive constant, and submatrices whose entries are well fit by a two-way ANOVA model. We identify size thresholds and associated (asymptotic) probability bounds for both large-average and ANOVA-fit submatrices. Read More

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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3816128PMC
http://dx.doi.org/10.3150/11-bej394DOI Listing
January 2013
4 Reads

Empirical likelihood-based tests for stochastic ordering.

Bernoulli (Andover) 2013 ;19(1):295-307

Department of Statistics and Computer Information Systems, Baruch College, The City University of New York, One Baruch Way, New York, NY 10010, USA.

This paper develops an empirical likelihood approach to testing for the presence of stochastic ordering among univariate distributions based on independent random samples from each distribution. The proposed test statistic is formed by integrating a localized empirical likelihood statistic with respect to the empirical distribution of the pooled sample. The asymptotic null distribution of this test statistic is found to have a simple distribution-free representation in terms of standard Brownian bridge processes. Read More

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http://dx.doi.org/10.3150/11-BEJ393SUPPDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3716296PMC
January 2013
4 Reads

Inference for modulated stationary processes.

Bernoulli (Andover) 2013 Feb;19(1):205-227

Department of Statistics, Penn State University, University Park, PA 16802.

We study statistical inferences for a class of modulated stationary processes with time-dependent variances. Due to non-stationarity and the large number of unknown parameters, existing methods for stationary or locally stationary time series are not applicable. Based on a self-normalization technique, we address several inference problems, including self-normalized central limit theorem, self-normalized cumulative sum test for the change-point problem, long-run variance estimation through blockwise self-normalization, and self-normalization-based wild boot-strap. Read More

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http://dx.doi.org/10.3150/11-BEJ399DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3607552PMC
February 2013
6 Reads

Consistent group selection in high-dimensional linear regression.

Bernoulli (Andover) 2010 Nov;16(4):1369-1384

Department of Mathematics, University of West Georgia, 1601 Maple Street, Carrollton, GA 30118, USA.

In regression problems where covariates can be naturally grouped, the group Lasso is an attractive method for variable selection since it respects the grouping structure in the data. We study the selection and estimation properties of the group Lasso in high-dimensional settings when the number of groups exceeds the sample size. We provide sufficient conditions under which the group Lasso selects a model whose dimension is comparable with the underlying model with high probability and is estimation consistent. Read More

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http://dx.doi.org/10.3150/10-BEJ252DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3209717PMC
November 2010
1 Read

Simultaneous Critical Values For T-Tests In Very High Dimensions.

Bernoulli (Andover) 2011 Feb;17(1):347-394

Department of Statistics and Operations Research, 318 Hanes Hall, CB 3260, University of North Carolina at Chapel Hill, Chapel Hill, NC, 27599.

This article considers the problem of multiple hypothesis testing using t-tests. The observed data are assumed to be independently generated conditional on an underlying and unknown two-state hidden model. We propose an asymptotically valid data-driven procedure to find critical values for rejection regions controlling k-family wise error rate (k-FWER), false discovery rate (FDR) and the tail probability of false discovery proportion (FDTP) by using one-sample and two-sample t-statistics. Read More

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http://dx.doi.org/10.3150/10-BEJ272DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3092179PMC
February 2011
2 Reads

Nonparametric estimation of a convex bathtub-shaped hazard function.

Bernoulli (Andover) 2009 Nov;15(4):1010-1035

Department of Mathematics and Statistics, N520 Ross Building, 4700 Keele Street, York University, Toronto, ON, Canada M3J 1P3.

In this paper, we study the nonparametric maximum likelihood estimator (MLE) of a convex hazard function. We show that the MLE is consistent and converges at a local rate of n(2/5) at points x(0) where the true hazard function is positive and strictly convex. Moreover, we establish the pointwise asymptotic distribution theory of our estimator under these same assumptions. Read More

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http://dx.doi.org/10.3150/09-BEJ202DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2850000PMC
November 2009
3 Reads

Variable Selection in Measurement Error Models.

Authors:
Yanyuan Ma Runze Li

Bernoulli (Andover) 2010 ;16(1):274-300

Department of Statistics, Texas A&M University, College Station, TX 77843.

Measurement error data or errors-in-variable data are often collected in many studies. Natural criterion functions are often unavailable for general functional measurement error models due to the lack of information on the distribution of the unobservable covariates. Typically, the parameter estimation is via solving estimating equations. Read More

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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2832228PMC
http://dx.doi.org/10.3150/09-bej205DOI Listing
January 2010
5 Reads

The central limit theorem under random truncation.

Bernoulli (Andover) 2008 Aug;14(3):604-622

Mathematical Institute, University of Giessen, Arndtstr. 2, D-35392 Giessen, Germany.

Under left truncation, data (X(i), Y(i)) are observed only when Y(i) ≤ X(i). Usually, the distribution function F of the X(i) is the target of interest. In this paper, we study linear functionals ∫ φ dF(n) of the nonparametric maximum likelihood estimator (MLE) of F, the Lynden-Bell estimator F(n). Read More

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http://projecteuclid.org/euclid.bj/1219669622
Publisher Site
http://dx.doi.org/10.3150/07-BEJ116DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3404856PMC
August 2008
6 Reads
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