The empirical Bayes (EB) estimator or empirical best linear unbiased predictor (EBLUP) in the linear mixed model (LMM) is useful for the small area estimation in the sense of increasing the precision of estimation of small area means. However, one potential difficulty of EB is that when...

Case-cohort designs provide a cost effective way to conduct epidemiological follow-up studies in which event times are the outcome variables. This paper develops a quantile regression approach to the analysis of case-cohort data. Quantile regression is a highly useful tool to delineate...

Motivated by the problem of nonparametric inference in high level digital image analysis, we introduce a general extrinsic approach for data analysis on Hilbert manifolds with a focus on means of probability distributions on such sample spaces. To perform inference on these means, we appeal to...

Bootstrap is the standard method in the spatial scan test. However, because the spatial scan statistic lacks theoretical properties, its development and connection to mainstream statistics has been limited. Using the methods of empirical processes with a few weak regularity conditions, the...

Consider the problem of testing a linear hypothesis of regression coefficients in a general linear regression model with a covariance matrix involving several nuisance parameters. Then, the Bartlett-type adjustments of the Wald, Score, and modified Likelihood Ratio tests are derived for general...

In this paper, we are interested in an estimation problem concerning the mean parameter of a random matrix whose distribution is elliptically contoured. We derive two general formulas for the bias and risk functions of a class of multidimensional shrinkage-type estimators. As a by product, we...

The general maximum likelihood empirical Bayes (GMLEB) method has been proven to possess optimal properties and demonstrated to have superior numerical performance in the Gaussian sequence model. Although it is known that nonparametric function estimation and the Gaussian sequence models are...

Most models for categorical data rely on linear models in which higher order interactions are limited, usually to second order terms. Here we explore a dataset where second order interactions lead unavoidably to high order interactions. However in certain cases these interactions have a simple...

In this paper, we propose a general spiked model called the power spiked model in high-dimensional settings. We derive relations among the data dimension, the sample size and the high-dimensional noise structure. We first consider asymptotic properties of the conventional estimator of...

This paper derives tests for skewness and kurtosis for the panel data one-way error component model. The test statistics are based on the between and within transformations of the pooled OLS residuals, and are derived in a moment conditions framework. We establish the limiting distribution of...