A distributional mixing condition is introduced for stationary sequences of random vectors to study their extremes. For a sequence satisfying the condition, the following topics which concern the weak limit F of properly normalized partial maxima are studied: (1) To obtain characterizations of...

Conditions are obtained for the multivariate components of variance model to admit a multivariate analysis of variance (MANOVA). MANOVA in this setup is defined as a partition of the sum of squares and sum of products matrix into independent Wishart matrices. A minimal sufficient statistic is...

A class of rank estimators of treatment effects in a two-way MANOVA model without interaction is considered. Asymptotic distributions of the R-estimators as the number of blocks tends to infinity are derived. Based on the R-estimators and their asymptotic distributions, confidence regions for...

Bivariate exponential distribution of Marshall-Olkin form, bivariate Rayleigh distribution, and bivariate Weibull distribution have been characterized through some functional equations to be satisfied by the survival function and hazard function.

In this paper, the authors studied certain properties of the estimate of Liang and Krishnaiah (1985, J. Multivariate Anal. 16, 162-172) for multivariate binary density. An alternative shrinkage estimate is also obtained. The above results are generalized to general orthonormal systems.

Series expansions and second-order asymptotic expansions are obtained for the characteristic functions of three statistics useful for testing the independence of two multivariate regression equations with different design matrices.

We apply the Malliavin calculus to study several non-degeneracy conditions on the coefficients of a stochastic differential equation on the plane, in order to deduce the existence and smoothness of density for the law of the solution.

Let M be a square integrable martingale indexed by [0, 1]2 with respect to a filtration which possesses the property of conditional independence. Assume that M has trajectories which are continuous for approach from the right upper quadrant and possess limits for the remaining three. M can have...

A class of linear serial multirank statistics is introduced for the problem of testing the null hypothesis that a multivariate series of observations is white noise (with unspecified density function) against alternatives of ARMA dependence. The asymptotic distributional properties of these...

Hypothesis testing problems are studied when invariance under suitable groups of transformations exist. Both compact and locally compact groups are considered. Expressions for the lower bounds on Bayes factors are derived under fairly general conditions. It is shown that the lower bounds can be...