We determine Riemannian distances between a large class of multivariate probability densities with the same mean, where the Riemannian metric is induced by a weighted Fisher information matrix. We reduce the evaluation of distances to quadrature and in some cases give closed form expressions.

In the paper we study a semiparametric density estimation method based on the model of an elliptical distribution. The method considered here shows a way to overcome problems arising from the curse of dimensionality. The optimal rate of the uniform strong convergence of the estimator under...

This paper aims to investigate the constraints on dependence measures based on the concept of concordance when discrete random variables are involved. The main technical argument consists in a continuous extension of integer-valued random variables by convolution with unit support kernels.

This note formalizes some analytical results on the n-dimensional multivariate truncated normal distribution where truncation is one-sided and at an arbitrary point. Results on linear transformations, marginal and conditional distributions, and independence are provided. Also, results on...

The popularity of state-space models comes from their flexibilities and the large variety of applications they have been applied to. For multivariate cases, the assumption of normality is very prevalent in the research on Kalman filters. To increase the applicability of the Kalman filter to a...

A new class of multivariate skew-normal distributions, fundamental skew-normal distributions and their canonical version, is developed. It contains the product of independent univariate skew-normal distributions as a special case. Stochastic representations and other main properties of the...

We study the conditions under which the sample mean is self-consistent, and therefore an optimal predictor, for an arbitrary observation in the sample.

The aim of this paper is to propose a simple method in order to evaluate the (approximate) distribution of matrix quadratic forms when Wishartness conditions do not hold. The method is based upon a factorization of a general Gaussian stochastic matrix as a special linear combination of...

Given a random sample from a continuous variable, it is observed that the copula linking any pair of order statistics is independent of the parent distribution. To compare the degree of association between two such pairs of ordered random variables, a notion of relative monotone regression...

Objective functions that are applied in ordinal data analysis must be adequate, i.e. carefully adapted to the structure of the observed data. In addition, any analysis of data that is based upon objective functions must lead to interpretable results. After a general characterization of adequate...