One of the most useful tools for handling multivariate distributions with givenunivariatemarginals is the copula function. Using it, any multivariate distribution function can be represented in a way that emphasizes the separate roles of the marginals and of the dependence structure. The goal of...

Liang and Zeger introduced a class of estimating equations that gives consistent estimates of regression parameters and of their variances in the class of generalized linear models for longitudinal data. When the response variable in such models is subject to overdispersion, the oerdispersion...

We consider the asymptotic analysis of penalized likelihood type estimators for generalized nonparametric regression problems in which the target parameter is a vector-valued function defined in terms of the conditional distribution of a response given a set of covariates. A variety of examples...

We address the classification problem where an item is declared to be from population[pi]jif certain of its characteristicsvare assumed to be sampled from the distribution with pdf fj(v|[theta]j), wherej=1, 2, ..., m. We first solve the two population classification problem and then...

For thed-dimensional empirical process and thed-dimensional homogeneous Poisson process we give weak laws for the maximal and minimal number of points in unions of sets from certain families.

Under minimum assumptions on the stochastic regressors, strong consistency of Bayes estimates is established in stochastic regression models in two cases: (1) When the prior distribution is discrete, the p.d.f.fof i.i.d. random errors is assumed to have finite Fisher informationI=[integral...

This paper considers asymptotic expansions of certain expectations which appear in the theory of large deviation for Gaussian random vectors with values in a separable real Hilbert space. A typical application is to calculation of the "tails" of distributions of smooth...

In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model ), preliminary test estimator (PTE) based on a test of the model , shrinkage estimator (SE) and...

Generalizing recent work of P. C. Matthews and A. L. Rukhin (Ann. Appl. Probab.3(1993), 454-466), we obtain the limit law of the largest interpoint Euclidean distance for a spherically symmetric multivariate sample of the Kotz distribution. While going through the proof, some errors in the...

We present a method of projections onto convex cones for establishing the sharp bounds in terms of the first two moments for the expectations ofL-estimates based on samples from restricted families. In this part, we consider the case of possibly dependent identically distributed parent random...