The geometrical convergence of the Gibbs sampler for simulating a probability distribution inRdis proved. The distribution has a density which is a bounded perturbation of a log-concave function and satisfies some growth conditions. The analysis is based on a representation of the Gibbs sampler...

We give a complete description of the rate of strong consistency of the scaled and unscaled total time on test curves, which are fundamental notions in the statistical theory of reliability and life testing. The proof is crucially based on the general Vervaat process.

The model-building problem of periodically correlatedm-variateq-dependent processes is considered. We show that for a given periodical autocovariance function of anm-variateMA(q) process there are two particular corresponding classes (that may reduce to one class) of periodic (equivalent)...

Let (X, Y) be an d--valued regression pair, whereXhas a density andYis bounded. Ifni.i.d. samples are drawn from this distribution, the Nadaraya-Watson kernel regression estimate in dwith Hilbert kernelK(x)=1/||x||dis shown to converge weakly for all such regression pairs. We also show that...

This article describes a local parameterization of orthogonal and semi-orthogonal matrices. The parameterization leads to a unified approach for obtaining the asymptotic joint distributions of estimators of singular-values and -vectors, and of eigen-values and -vectors. The singular- or...

The local dependence function is constant for the bivariate normal distribution. Here we identify all other distributions which also have constant local dependence. The key property is exponential family conditional distributions and a linear conditional mean. When given two marginal...

We consider the problem of estimating the shape parameters in the multi- variate Liouville model in the presence of an unknown infinite-dimensional parameter. We propose an ad hoc estimate and show that it is asymptotically efficient.

Kingman showed that if the vectorXNis distributed according to the Dirichlet law then the vector of descending order statistics converges, under certain conditions, to a nondegenerate limit. This contrasts with the fact that the limit of any fixed component ofXNis zero. Nevertheless,XNdoes have,...

We consider bivariate logspline density estimation for tomography data. In the usual logspline density estimation for bivariate data, the logarithm of the unknown density function is estimated by tensor product splines, the unknown parameters of which are given by maximum likelihood. In this...

In this paper we investigate performances of the test of multinormality introduced by Malkovich and Afifi. An approximation formula of the power of the test against elliptically symmetric distributions is derived. Examples which illustrate the present results are also discussed.