Mehler gave an expansion for the standard bivariate normal density. Kibble extended it to a multivariate normal density whose covariance is a correlation matrix. We give extensions of these expansions for general covariances.

Consider the empirical spectral distribution of complex random nxn matrix whose entries are independent and identically distributed random variables with mean zero and variance 1/n. In this paper, via applying potential theory in the complex plane and analyzing extreme singular values, we prove...

We develop methods to compare multiple multivariate normally distributed samples which may be correlated. The methods are new in the context that no assumption is made about the correlations among the samples. Three types of null hypotheses are considered: equality of mean vectors, homogeneity...

Ramachandran (1969) [9, Theorem 8] has shown that for any univariate infinitely divisible distribution and any positive real number [alpha], an absolute moment of order [alpha] relative to the distribution exists (as a finite number) if and only if this is so for a certain truncated version...

The empirical likelihood method is especially useful for constructing confidence intervals or regions of parameters of interest. Yet, the technique cannot be directly applied to partially linear single-index models for longitudinal data due to the within-subject correlation. In this paper, a...

Model selection by means of the predictive least squares (PLS) principle has been thoroughly studied in the context of regression model selection and autoregressive (AR) model order estimation. We introduce a new criterion based on sequentially minimized squared deviations, which are smaller...

In this paper we consider elliptical random vectors in with stochastic representation , where R is a positive random radius independent of the random vector which is uniformly distributed on the unit sphere of and is a given matrix. Denote by ||[dot operator]|| the Euclidean norm in , and let F...

This work presents a Bayesian semiparametric approach for dealing with regression models where the covariate is measured with error. Given that (1) the error normality assumption is very restrictive, and (2) assuming a specific elliptical distribution for errors (Student-t for example), may be...

In extreme value analysis, staring from Smith (1987) [1], the maximum likelihood procedure is applied in estimating the shape parameter of tails--the extreme value index [gamma]. For its theoretical properties, Zhou (2009) [12] proved that the maximum likelihood estimator eventually exists and...

For the well-known Fay-Herriot small area model, standard variance component estimation methods frequently produce zero estimates of the strictly positive model variance. As a consequence, an empirical best linear unbiased predictor of a small area mean, commonly used in small area estimation,...