A characterization for the positivityof the angle between past and future of multivariate stationary stochastic processes is established. In order to prove the results a lemma is proved which is of independent interest, and which is very useful in other areas of prediction theory as well.

In full rank multivariate exponential families of lattice distributions, one sided testing problems are considered. For these testing problems the uniformly most powerful unbiased tests are not uniformly efficient of order o(n-1) in the class 2* of all tests which are asymptotically similar of...

Let Rn-p, (n), Gl(p) and +(p) denote respectively the set of n-p matrices, the set of n-n orthogonal matrices, the set of p-p nonsingular matrices and the set of p - p positive definite matrices. In this paper, it is first shown that a bijective and bimeasurable transformation (BBT) g on...

In this paper, the authors propose procedures for detection of the number of signals in presence of Gaussian white noise under an additive model. This problem is related to the problem of finding the multiplicity of the smallest eigenvalue of the covariance matrix of the observation vector. The...

In the linear model Xn - 1 = Cn - p[theta]p - 1 + En - 1, Huber's theory of robust estimation of the regression vector [theta]p - 1 is adapted for two models for the partially specified common distribution F of the i.i.d. components of the error vector En - 1. In the first model considered, the...

The problem of prediction of wide sense stationary processes on 2 with respect to the column-by-column or row-by-row lexicographic order is studied. A theorem giving an explicit realization of the corresponding canonical factorization of the spectral density is proved and conditions are given...

Discrete versions of the mean integrated squared error (MISE) provide stochastic measures of accuracy to compare different estimators of regression fuctions. These measures of accuracy have been used in Monte Carlo trials and have been employed for the optimal bandwidth selection for kernel...

The necessary and sufficient condition for a function to be upper class relative to a Brownian motion process was obtained by T. Sirao and T. Nisida (1952, Nagoya Math. J. 4, 97-101) and a related result on first passage distribution was obtained by P. K. Sen and M. J. Wichura (in press,...

For a sequence of independent and identically distributed random vectors, upper and lower bounds are obtained for the discrepancy between the probability measure Pn, induced by their normalized sum, and the Normal measure [Phi]. The upper and lower bounds are of the same order of magnitude....

Let Xi, i = 1, be a sequence of [phi]-mixing random variables with values in a sample space (X, A). Let L(Xi) = P(i) for all i = 1 and let n, n = 1, be classes of real-valued measurable functions on (X, A). Given any function g on (X, A), let Sn(g) = [Sigma]i = 1n {g(Xi) - Eg(Xi)}. Under weak...