We apply the holonomic gradient method introduced by Nakayama et al. (2011) [23] to the evaluation of the exact distribution function of the largest root of a Wishart matrix, which involves a hypergeometric function 1F1 of a matrix argument. Numerical evaluation of the hypergeometric function...

A general moment bound for sums of products of Gaussian vector’s functions extending the moment bound in Taqqu (1977, Lemma 4.5) [28] is established. A general central limit theorem for triangular arrays of nonlinear functionals of multidimensional non-stationary Gaussian sequences is proved....

An estimator is said to be of orders0 if its bias has magnitude n−s, where n is the sample size. We give delta estimators and jackknife estimators of order four for smooth functions of the parameters of a multinomial distribution. An unbiased estimator is given for its density function. We...

The goal of this paper is to give explicit procedures and equations for performing metric multidimensional scaling to surfaces. More specifically, we describe a method for determining a configuration of points in a closed and orientable surface (i.e., the MDS space) for which the interpoint...

Two stochastic representations of multivariate geometric distributions are analyzed, both are obtained by lifting the lack-of-memory (LM) property of the univariate geometric law to the multivariate case. On the one hand, the narrow-sense multivariate geometric law can be considered a discrete...

We present arguments in favor of the inequalities var(Xn2∣X∈Bv(ρ))≤2λnE[Xn2∣X∈Bv(ρ)], where X∼Nv(0,Λ) is a normal vector in v≥1 dimensions, with zero mean and covariance matrix Λ=diag(λ), and Bv(ρ) is a centered v-dimensional Euclidean ball of square radius ρ. Such...

So-called pair copula constructions (PCCs), specifying multivariate distributions only in terms of bivariate building blocks (pair copulas), constitute a flexible class of dependence models. To keep them tractable for inference and model selection, the simplifying assumption, that copulas of...

The aim of this article is to present a non-parametric way to identify and estimate the unknown frequencies in the Fourier representation of mean function for almost periodically correlated time series. We state the exact form of asymptotic distribution of normalized estimator of Fourier...

In the development of nonlinear reproductive dispersion mixed models, it is commonly assumed that distribution of random effects is normal. The normality assumption is likely violated in many practical applications. In this paper, we assume that distribution of random effects is specified by a...

Motivated by the analysis of genetical genomic data, we consider the problem of estimating high-dimensional sparse precision matrix adjusting for possibly a large number of covariates, where the covariates can affect the mean value of the random vector. We develop a two-stage estimation...