In the problem of estimating the mean, [theta], of a multivariate normal distribution, an experimenter will often be able to give some vague prior specifications about [theta]. This information is used to construct confidence sets centered at improved estimators of [theta]. These sets are shown...

Edgeworth approximations for multivariate U-statistics hold up to the order o(n-1/2) under moment conditions and the assumption that the projection of the U-statistic to sums of i.i.d. random vectors is strongly nonlattice.

In this paper we examine the characterization of multivariate reciprocal stationary Gaussian processes in terms of their covariance matrix function. As an illustration, we identify all second-order reciprocal Gaussian processes.

In this note we derive the exact order of magnitude of the moments of the modulus of continuity for multiparameter Poisson and, almost as a corollary, for multivariate empirical processes.

We show how to renormalize the intersection local time of fractional Brownian motion of index [beta] in the plane, when½< [beta] <¾. When[beta] = ½, i.e., planar Brownian, such a renormalization is due to Varadhan.

Defined is a class of models which have the following property: If L'Y is an admissible estimator of C'EY among linear estimators, then there exists a matrix H such that L = HC and H'Y is an admissible estimator of EY. This class includes the regression model. A model which does not have this...

We deal with quantile processes based on intermediate order statistics. Using an approximation of the uniform quantile process in weighted metrics, we prove weak convergence of weighted and nonweighted intermediate quantile processes.

The optimal exponential rate at which the Type II error probability of a multivariate linear hypothesis test can tend to zero while the Type I error probability is held fixed is given. The likelihood ratio test, the test of Hotelling and Lawley, the test of Bartlett, Nanda, and Pillai, and the...

A general integral expression is obtained for evaluating the performance of Fisher's linear discriminant function applied to spherical distributions (SD). Recurrence relations are given for certain special cases including the spherical gamma, Pearson VII, and generalized Laplace distributions....

We develop a unified theory for obtaining stochastic rearrangement inequalities and show how this theory may be applied in statistical contexts such as ranking problems, hypothesis testing, contamination models, and optimal assembly of systems.