In this paper, we apply Grenader's method of sieves to the problem of estimation of the infinite dimensional mean parameter of a Gaussian random vector with values in a real separable Banach space. We use an increasing sequence of natural sieves in terms of geometric properties of the parameter...

Asymptotic confidence bounds on the location parameters of the linear growth curve, asymptotic distribution of the canonical correlations and asymptotic confidence bounds on the discriminatory value for the linear discriminant function are established when a set of independent observations are...

The problem of testing equality of two normal covariance matrices, [Sigma]1 = [Sigma]2 is studied. Two alternative hypotheses, [Sigma]1 [not equal to] [Sigma]2 and [Sigma]1 - [Sigma]2 0 are considered. Minimal complete classes among the class of invariant tests are found. The group of...

It is well known that a univariate counting process with a given intensity function becomes Poisson, with unit parameter, if the original time parameter is replaced by the integrated intensity. P. A. Meyer (in Martingales (H. Dinges, Ed.), pp. 32-37. Lecture Notes in Mathematics, Vol. 190,...

This paper introduces a one-parameter bivariate family of distributions whose marginals are arbitrary and which include Fréchet bounds as well as the distribution corresponding to independent variables. Some geometrical and statistical properties on the stochastic dependence parameter are...

Motivated by the analysis of linear rank estimators and the Buckley-James nonparametric EM estimator in censored regression models, we study herein the asymptotic properties of stochastic integrals of certain two-parameter empirical processes. Applications of these results on empirical processes...

A uniform estimate of the rate of convergence in the central limit theorem (CLT) in certain Banach spaces for dependent random variables is established when the Gaussian measure of the [epsilon]-neighbourhood of the boundary of a set is proportional to [epsilon] and the third order moment is...

A real valued function of s vector arguments in Rn is said to be arrangement increasing if the function increases in value as the components of the vector arguments become more similarly arranged. Various examples of arrangement increasing functions are given including many joint multivariate...

The paper is concerned with estimating multivariate linear and autoregressive models using a generalisation of the functional least-squares procedure. This leads to a family of estimators, indexed by a vector parameter, for which strong uniform consistency and weak convergence results are...