Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. This is known as large p small n problem. Furthermore, the problem is more complicated when we have multiple correlated responses. We develop multivariate...

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...

In the context of the Fay–Herriot model, a mixed regression model routinely used to combine information from various sources in small area estimation, certain adjustments to a standard likelihood (e.g., profile, residual, etc.) have been recently proposed in order to produce strictly positive...

In this paper, we describe and study a class of linear shrinkage estimators of the covariance matrix that is well-suited for high dimensional matrices, has a rather wide domain of applicability, and is rooted into the Gaussian conjugate framework of Chen (1979). We propose here a new look at...

Many multiple testing procedures make use of the p-values from the individual pairs of hypothesis tests, and are valid if the p-value statistics are independent and uniformly distributed under the null hypotheses. However, it has recently been shown that these types of multiple testing...

In this paper we study a monotone regularized kernel general empirical Bayes method for the estimation of a vector of normal means. This estimator is used to improve upon the kernel methods of Zhang (1997) [12] and Brown and Greenshtein (2009) [5]. We prove an oracle inequality for the regret of...

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...

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...

It is crucial to check validation of any statistical model after fitting it for a given set of data. In Bayesian statistics, a researcher can check the fit of the model using a variety of strategies. In this paper we consider two major aspects, first checking that the posterior inferences are...

Many parameters and positive-definiteness are two major obstacles in estimating and modeling a correlation matrix for longitudinal data. In addition, when longitudinal data is incomplete, incorrectly modeling the correlation matrix often results in bias in estimating mean regression parameters....