In the problem of selecting the explanatory variables in the linear mixed model, we address the derivation of the (unconditional or marginal) Akaike information criterion (AIC) and the conditional AIC (cAIC). The covariance matrices of the random effects and the error terms include unknown...

Support vector machines (SVMs) have attracted much attention in theoretical and in applied statistics. The main topics of recent interest are consistency, learning rates and robustness. We address the open problem whether SVMs are qualitatively robust. Our results show that SVMs are...

By combining the findings of two recent, seminal papers by Nualart, Peccati and Tudor, we get that the convergence in law of any sequence of vector-valued multiple integrals Fn towards a centered Gaussian random vector N, with given covariance matrix C, is reduced to just the convergence of: (i)...

Multivariate tree-indexed Markov processes are discussed with applications. A Galton-Watson super-critical branching process is used to model the random tree-indexed process. Martingale estimating functions are used as a basic framework to discuss asymptotic properties and optimality of...

Let be a stationary process with mean 0 and finite variances, let [phi]h=E(XkXk+h) be the covariance function and its usual estimator. Under mild weak dependence conditions, the distribution of the vector is known to be asymptotically Gaussian for any , a result having important statistical...

This article analyzes whether some existing tests for the pxp covariance matrix [Sigma] of the N independent identically distributed observation vectors work under non-normality. We focus on three hypotheses testing problems: (1) testing for sphericity, that is, the covariance matrix [Sigma] is...

U-quantiles are applied in robust statistics, like the Hodges-Lehmann estimator of location for example. They have been analysed in the case of independent random variables with the help of a generalized Bahadur representation. Our main aim is to extend these results to U-quantiles of strongly...

This paper suggests a new technique to construct first order Markov processes using products of copula functions, in the spirit of Darsow et al. (1992) [10]. The approach requires the definition of (i) a sequence of distribution functions of the increments of the process, and (ii) a...

Let be a pxp random matrix having a Wishart distribution . For testing a general covariance structure , we consider a class of test statistics , where is a distance measure from to , [lambda]i's are the eigenvalues of , and h is a given function with certain properties. Wakaki, Eguchi and...

An additive model-assisted nonparametric method is investigated to estimate the finite population totals of massive survey data with the aid of auxiliary information. A class of estimators is proposed to improve the precision of the well known Horvitz-Thompson estimators by combining the spline...