Search Our Scientific Publications & Authors

Ann Inst Stat Math 2015 Feb;67(1):93-127

Purdue University and North Carolina State University.

We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on the nonparametric component and shrinkage penalty on the parametric components, which can achieve function smoothing and sparse estimation simultaneously. We establish the convergence rate and oracle properties of the estimator under weak regularity conditions. Read More

Ann Inst Stat Math 2014 Feb;66(1):1-31

Department of Statistical Science, Duke University,

We consider the problem of robust Bayesian inference on the mean regression function allowing the residual density to change flexibly with predictors. The proposed class of models is based on a Gaussian process prior for the mean regression function and mixtures of Gaussians for the collection of residual densities indexed by predictors. Initially considering the homoscedastic case, we propose priors for the residual density based on probit stick-breaking (PSB) scale mixtures and symmetrized PSB (sPSB) location-scale mixtures. Read More

Ann Inst Stat Math 2013 Oct;65(5):807-832

Division of Biostatistics, University of Minnesota, Minneapolis, MN 55455.

High-dimensional feature selection has become increasingly crucial for seeking parsimonious models in estimation. For selection consistency, we derive one necessary and sufficient condition formulated on the notion of degree-of-separation. The minimal degree of separation is necessary for any method to be selection consistent. Read More

Ann Inst Stat Math 2012 Aug;64(4):751-764

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

We revisit the second-order nonlinear least square estimator proposed in Wang and Leblanc (Anne Inst Stat Math 60:883-900, 2008) and show that the estimator reaches the asymptotic optimality concerning the estimation variability. Using a fully semiparametric approach, we further modify and extend the method to the heteroscedastic error models and propose a semiparametric efficient estimator in this more general setting. Numerical results are provided to support the results and illustrate the finite sample performance of the proposed estimator. Read More

Ann Inst Stat Math 2012 Aug 18;64(4):687-714. Epub 2011 Nov 18.

Indian Statistical Institute, 203 B.T. Road, Kolkata, W.B. 700108, India.

This article considers a broad class of kernel mixture density models on compact metric spaces and manifolds. Following a Bayesian approach with a nonparametric prior on the location mixing distribution, sufficient conditions are obtained on the kernel, prior and the underlying space for strong posterior consistency at any continuous density. The prior is also allowed to depend on the sample size n and sufficient conditions are obtained for weak and strong consistency. Read More

Ann Inst Stat Math 2012 Apr;64(2):415-438

Academy of Mathematics and Systems Science, Chinese Academy of Science Beijing 100080, China.

Hazard function estimation is an important part of survival analysis. Interest often centers on estimating the hazard function associated with a particular cause of death. We propose three nonparametric kernel estimators for the hazard function, all of which are appropriate when death times are subject to random censorship and censoring indicators can be missing at random. Read More

Ann Inst Stat Math 2011 Jun;63(3):497-509

Division of Epidemiology & Biostatistics, School of Public Health, University of Illinois at Chicago, 1603 West Taylor Street, Chicago, IL 60612.

We derive new representations of the efficient score for coarse data problems based on Neumann series expansion. The representations can be applied to both ignorable and nonignorable coarse data. An approximation to the new representation may be used for computing locally efficient scores in such problems. Read More

Ann Inst Stat Math 2011 Feb;63(1):81-99

Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK 99775, USA.

We present a deconvolution estimator for the density function of a random variable from a set of independent replicate measurements. We assume that measurements are made with normally distributed errors having unknown and possibly heterogeneous variances. The estimator generalizes the deconvoluting kernel density estimator of Stefanski and Carroll (1990), with error variances estimated from the replicate observations. Read More

Ann Inst Stat Math 2011 Feb;63(1):59-80

Department of Biostatistics, Harvard School of Public Health, 655 Huntington Ave. Bldg 2, Room 435A, Boston, MA 02115, USA.

As a generalization of the Dirichlet process (DP) to allow predictor dependence, we propose a local Dirichlet process (lDP). The lDP provides a prior distribution for a collection of random probability measures indexed by predictors. This is accomplished by assigning stick-breaking weights and atoms to random locations in a predictor space. Read More

Ann Inst Stat Math 2010 Feb;62(1):11-35

We propose a method for selecting variables in latent class analysis, which is the most common model-based clustering method for discrete data. The method assesses a variable's usefulness for clustering by comparing two models, given the clustering variables already selected. In one model the variable contributes information about cluster allocation beyond that contained in the already selected variables, and in the other model it does not. Read More

Ann Inst Stat Math 2010 Jun;62(3):487-514

Department of Statistics and Applied Probability, National University of Singapore, Singapore 117546, Singapore.

We consider the median regression with a LASSO-type penalty term for variable selection. With the fixed number of variables in regression model, a two-stage method is proposed for simultaneous estimation and variable selection where the degree of penalty is adaptively chosen. A Bayesian information criterion type approach is proposed and used to obtain a data-driven procedure which is proved to automatically select asymptotically optimal tuning parameters. Read More

Ann Inst Stat Math 2009 Mar;61(1):27-46

Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY 14642, USA.

In this article we consider a semiparametric generalized mixed-effects model, and propose combining local linear regression, and penalized quasilikelihood and local quasilikelihood techniques to estimate both population and individual parameters and nonparametric curves. The proposed estimators take into account the local correlation structure of the longitudinal data. We establish normality for the estimators of the parameter and asymptotic expansion for the estimators of the nonparametric part. Read More

Ann Inst Stat Math 2009 Feb;100(2):278-290

Department of Statistics and Actuarial Science, University of Waterloo, Canada N2L 3G1.

Clustered data arise commonly in practice and it is often of interest to estimate the mean response parameters as well as the association parameters. However, most research has been directed to inference about the mean response parameters with the association parameters relegated to a nuisance role. There is little work concerning both the marginal and association structures, especially in the semiparametric framework. Read More