Estimators for the mean of polynomial weakly stationary sequences are developed and studied with respect to consistency and efficiency. These mean estimators are then applied to obtain 'better' estimators for the mean of weakly stationary sequences.

Let (Xi, Yi, Zi), i = 1, 2, ..., m, be a number of independent random vectors each with a non-singular trivariate normal distribution function with non-zero correlations and zero means. Let (X, Y, Z) be their maximum, i.e., X = maxiXi, Y = maxiYi, and Z = maxiZi. In this paper, we show that the...

Let (x, X[beta], V) be a linear model and let A' = (A'1, A'2) be a p - p nonsingular matrix such that A2X = 0, Rank A2 = p - Rank X. We represent the BLUE and its covariance matrix in alternative forms under the conditions that the number of unit canonical correlations between y1 ( = A1x) and y2...

The variational representation of the conditional expectation of a Gaussian signal X given observations Y corrupted by independent white noise is investigated in the general infinite-dimensional setting. Under Hilbert-Schmidt type assumptions it is shown that the filter can be realized on sample...

Central limit theorems are proved for Markov chains on the nonnegative integers that are homogeneous with respect to a sequence of orthogonal polynomials where the 3-term recurrence formula that defines the orthogonal polynomials has to satisfy some conditions. In particular, from the rate of...

By modifying the method of projection, the results of Hajek and Huskova are extended to show the asymptotic normality of signed and linear rank statistics under general alternatives for dependent random variables that can be expressed as independent vectors of fixed equal length. The score...

The Riemann space whose elements are m - k (m = k) matrices X such that X'X = Ik is called the Stiefel manifold and denoted by Vk,m. Some distributions on Vk,m, e.g., the matrix Langevin (or von Mises-Fisher) and Bingham distributions and the uniform distribution, have been defined and discussed...

The martingale methods of estimation are extended to point processes on the plane. A likelihood function is constructed and a general exponential formula is given. A central limit theorem is proved for processes which are both 1- and 2-martingales. Martingale estimators are defined, and...

Let ZN, N = 1, denote the integer lattice points in the N-dimensional Euclidean space. Asymptotic normality of kernel estimators of the multivariate density of stationary random fields indexed by ZN is established. Appropriate choices of the bandwiths are found. The random fields are assumed to...

Let X1, ..., Xn be independent random variables and define for each finite subset I [subset of] {1, ..., n} the [sigma]-algebra = [sigma]{Xi : i [epsilon] I}. In this paper -measurable random variables WI are considered, subject to the centering condition E(WI [short parallel] ) = 0 a.s. unless...