Equivariant estimation of the multivariate scatter of a random vector X can be derived from a criterion of (lack of) spherical symmetry g(X). The scatter matrix is V = (ATA)-1, where A is the transformation matrix which makes AX as spherical as possible, that is, which minimizes g(AX). The new...

We examine the second-order structure arising when a symmetric function is evaluated over intersecting subsets of random variables. The original work of Hoeffding is updated with reference to later results. New representations and inequalities are presented for covariances and applied to...

A general class of Fuller modified maximum likelihood estimators are considered. It is shown that this class possesses finite moments. Asymptotic bias and asymptotic mean squared error are derived using small-[sigma] expansions. A simulation study is carried out to compare different estimators...

The maximum likelihood estimation of the unknown parameter of a diffusion process based on an approximate likelihood given by the discrete observation is treated when the diffusion coefficients are unknown and the condition for "rapidly increasing experimental design" is broken. The asymptotic...

A central limit theorem is proved for a class of U-statistics whose kernel depends on the sample size and for which the projection method may fail, since several terms in the Hoeffding decomposition contribute to the limiting variance. As an application we derive the asymptotic normality of the...

A class of generalized linear rank statistics is introduced for regression analysis in the presence of truncation or censoring on the response variable. Applications of these statistics to hypothesis testing and estimation are discussed. Martingale theory and stochastic integrals of...

The Hölder classes [Lambda]a of vector-valued functions are defined. The functions in each space [Lambda]a are completely characterized by conditions concerning the decay of their Fourier coefficients, their smoothness, and their approximability by polynomials. It is shown that, in some sense,...

This paper provides a method of constructing multivariate distributions where both univariate marginals and a correlation matrix are given. An extension to multivariate marginals and a given intercorrelation matrix is also obtained. This method yields a family of distributions which are totally...

The problem of estimating the p - 1 mean vector [theta] based on two independent normal vectors Y1 ~ Np([theta], [sigma]2I) and Y2 ~ Np([theta], [xi][sigma]2I) is considered. For p = 3, when [xi] and [sigma]2 are unknown, it was shown by George (1991, Ann. Statist.) that under certain conditions...

Consider the fixed regression model with general weights, and suppose that the error random variables are coming from a strictly stationary stochastic process, satisfying the strong mixing condition. The asymptotic normality of the proposed estimate is established under weak conditions. The...