We discuss the capacity of the Gaussian channel with feedback. In general it is not easy to give an explicit formula for the capacity of a Gaussian channel, unless the channel is without feedback or a white Gaussian channel. We consider the case where a constraint, given in terms of the...

Let S be distributed as noncentral Wishart given by Wp(m, [Sigma], [Omega]) and let x be an n - 1 random vector distributed as N([mu], V). If qi = x'Aix + 2l'ix + ci, i = 1, 2,..., p, are p dependent second degree polynomials in the elements of x where Aj's are symmetric matrices, then the...

Weak invariance principles for certain continuous time parameter stochastic processes (including martingales and reverse martingales) are considered. Weak convergence in the sup-norm metric is also studied.

Indirect censoring is defined as the effect on observed variables of censoring on unobserved variables. Methods of testing for indirect censoring are discussed, and exemplified, using a bivariate Farlie-Gumbel-Morgenstern distribution.

We here extend our results on asymptotically Bayes risk efficient classification to the general regression scenario. More precisely, we find Lp consistent estimators for an arbitrary regression function provided only that the dependent variable has a finite absolute pth moment. The estimators...

Let (X, Y) be an d - -valued random vector and let (X1, Y1),...,(XN, YN) be a random sample drawn from its distribution. Divide the data sequence into disjoint blocks of length l1, ..., ln, find the nearest neighbor to X in each block and call the corresponding couple (Xi*, Yi*). It is shown...

A characterization of Gaussian subspaces of L2 is given. It is shown that Gaussian subspaces are essentially characterized by the property that all linear isometries are induced by measure-preserving transformations.

We treat situations in which independent structurally identical decision problems are to be faced either simultaneously or serially. Recent work on such compound decision problems has centered on finding procedures that satisfy the strengthened asymptotic optimality property of Gilliland and...

For certain types of stochastic processes {Xn n [set membership, variant] }, which are integrable and adapted to a nondecreasing sequence of [sigma]-algebras n on a probability space ([Omega], , P), several authors have studied the following problems: IfSdenotes the class of all stopping times...

The inverted complex Wishart distribution and its use for the construction of spectral estimates are studied. The density, some marginals of the distribution, and the first- and second-order moments are given. For a vector-valued time series, estimation of the spectral density at a collection of...