We consider the problem of estimating a p-dimensional vector [mu]1 based on independent variables X1, X2, and U, where X1 is Np([mu]1, [sigma]2[Sigma]1), X2 is Np([mu]2, [sigma]2[Sigma]2), and U is [sigma]2[chi]2n ([Sigma]1 and [Sigma]2 are known). A family of minimax estimators is proposed....

Same explicit optimal coupling results are derived with respect to minimal metrics of lp-type. In particular, the optimality of radial transformations, positive transformations, and monotone transformations of the components is established.

The problem of estimating the k-dimensional parameter vector in a linear regression model with m linear restrictions is considered. The proposed estimators are generalized Bayes with respect to a prior distribution compatible with the linear restrictions. Under certain conditions some of the...

In the random censorship from the right model, we prove a strong approximation result for the Bahadur-Kiefer-type process based on the product limit estimator. We derive from this strong approximation the pointwise rate of consistency of the corresponding Bahadur-Kiefer-type statistic.

Let Vk,m denote the Stiefel manifold whose elements are m - k (m = k) matrices X such that X'X = Ik. We may be interested in high dimensional (as m -- [infinity]) asymptotic behaviors of statistics on Vk,m. High dimensional Stiefel manifolds may appear in a geometrical study in other contexts,...

Burg's maximum entropy spectrum given the first p + 1 autocovariances is the spectrum of an autoregressive process of order p. The purpose of this paper is to present a multivariate version of Burg's spectrum.

In recent papers, Johnson and Kotz (Amer. Statist.44, 245-249 (1990); Math. Sci.15, 42-52 (1990)) have explored the utility of moment calculations as a simple way of establishing distributional forms. In particular a characterization theorem for beta distributions has been proved. In this paper...

Gaussian limits of processes with values in type 2 Banach spaces can be used to construct asymptotic confidence regions of spherical shape. This is done by estimating the covariance of the limit distribution. Nuclearity of the covariance operators makes it possible to work in subspaces of...

The problem of predicting the value of a linear function of future values of a stationary process when its past and present are known is considered. The estimator of a studied function is constructed which is expressed-through the set of canonical variables.

Using a perturbation of the rate of a Poisson process and an inverse time change, an integration by parts formula is obtained. This enables a new form of the integrand in a martingale representation result to be obtained.