For the Gaussian channel Y(t) = [Phi]([xi](s), Y(s); s [less, double equals] t) + X(t), the mutual information I([xi], Y) between the message [xi](·) and the output Y(·) is evaluated, where X(·) is a Gaussian noise. Furthermore, the optimal coding under average power constraints is...

This study presents methods for estimating and testing hypotheses about linear functions of the unknown parameters in a generalization of the growth curve model which allows missing data. The estimators proposed are best asymptotically normal (BAN). A testing method for large samples is...

In this paper an asymptotic theory is developed for a new time series model which was introduced in a previous paper [5]. An algorithm for computing estimates of the parameters of this time series model is given, and it is shown that these estimators are asymptotically efficient in the sense...

In this paper, necessary and sufficient conditions for the regularity of a general (multivariate) stationary process are obtained. These subsume all the known criteria of regularity for such processes.

Nonanticipative linear transformations of the two-parameter Wiener process W are studied. It is shown that they induce measures equivalent to two-parameter Wiener measure and the corresponding Radon-Nikodym derivatives are calculated. A two-parameter extension of Girsanov's theorem is...

The structure of the nonlinear space of a spherically invariant process is studied and the problem of discriminating between two spherically invariant processes as well as the problem of nonlinear estimation for spherically invariant processes are solved.

For a multivariate normal distribution with unknown mean vector and unknown dispersion matrix, a sequential procedure for estimating the unknown mean vector is suggested. The procedure is shown to be asymptotically "risk efficient" in the sense of Starr (Ann. Math. Statist. (1966), 1173-1185),...

In this paper, results of Lai, Heyde, and Rohatgi concerning the convergence rates for the laws of large numbers are extended for the case of independent random variables taking values in a separable Banach space.

For a vector of (estimable) functionals of several independent distributions, sequential confidence ellipsoids (of bounded maximum width) based on a class of generalized U-statistics are studied. A stopping rule along with a procedure for choosing the component sample sizes at each stage is...

Let X be a random vector with values in n and a Gaussian density f. Let Y be a random vector whose density can be factored as k · f, where k is a logarithmically concave function on n. We prove that the covariance matrix of X dominates the covariance matrix of Y by a positive semidefinite...