The sensitivity of halfspace depth values and contours to perturbations of the underlying distribution is investigated. The influence function of the halfspace depth of any point x[set membership, variant]p is bounded and discontinuous; it is constant and positive when the perturbing observation...

Let {Xn, n[greater-or-equal, slanted]1} be a sequence of stationary negatively associated random variables, Sj(l)=[summation operator]li=1 Xj+i, Sn=[summation operator]ni=1 Xi. Suppose that f(x) is a real function. Under some suitable conditions, the central limit theorem and the weak...

In this paper an exploratory technique based on the diagonalization of cross-variogram matrices is described. Through the definition of a model for the analysis and simulation of multivariate spatial data, a test procedure for the assumption of isotropy of multivariate spatial data is proposed....

This paper is concerned with a study of robust estimation in principal component analysis. A class of robust estimators which are characterized as eigenvectors of weighted sample covariance matrices is proposed, where the weight functions recursively depend on the eigenvectors themselves. Also,...

Asymptotic distributions of U-statistics to test for possible changes in the distribution will be derived when the change occurred. We will show that for all possible types of kernels, symmetric, antisymmetric, degenerate, non-degenerate, the test statistics are asymptotically normally...

The problems of testing a normal covariance matrix and an interval estimation of generalized variance when the data are missing from subsets of components are considered. The likelihood ratio test statistic for testing the covariance matrix is equal to a specified matrix, and its asymptotic null...

Consider the partial linear model Yi=X[tau]i[beta]+g(Ti)+[var epsilon]i, i=1, ..., n, where [beta] is a p-1 unknown parameter vector, g is an unknown function, Xi's are p-1 observable covariates, Ti's are other observable covariates in [0, 1], and Yi's are the response variables. In...

Let [rho] be a nonnegative homogeneous function on n. General structure of the set of numerical pairs ([delta], [lambda]), for which the function (1-[rho][lambda](x))[delta]+ is positive definite on n is investigated; a criterion for positive definiteness of this function is given in terms of...

Asymptotic expansions for large deviation probabilities are used to approximate the cumulative distribution functions of noncentral generalized chi-square distributions, preferably in the far tails. The basic idea of how to deal with the tail probabilities consists in first rewriting these...

We give James-Stein type estimators of a multivariate normal mean vector by shrinkage towards a closed convex set K with a smooth or piecewise smooth boundary. The rate of shrinkage is determined by the curvature of the boundary of K at the projection point onto K. By considering a sequence of...