Let {X(t), -[infinity] < t < [infinity]} be a real-valued stationary process with a bivariate probability density function f(x1, x2; t), t > 0, and let {tj} be a renewal point processes on [0, [infinity]). Estimates of f(x1, x2; t), based on the discretetime observations {X(tj), tj}j = 1n, are considered and their statistical properties are investigated. The quadratic-mean consistency of and central limit...</t>

Using a technique originated by A. Olsen, J. Seely, and D. Birkes (Ann. Statist. 4 (1976), 878-890) and developed by L. R. LaMotte (Ann. Statist. 10 (1982), 245-256) we establish necessary conditions of C. R. Rao's type (Ann. Statist. 4 (1976), 1023-1037) for a linear estimator to be admissible...

Using two definitions of the conditional empirical processes we obtain some approximations for these processes. We also prove the functional law of the iterated logarithm for the conditional processes. Our results say that the asymptotic behavior of the conditional and unconditional empirical...

Let X = [sigma]Z be the scale mixture of Z with the scale factor [sigma] 0. We consider two type expansions G[delta],k(x) and [Phi][delta],k(x) as the approximations to the distribution function F(x) of X. In this paper we derive non-uniform error bounds in approximating F(x) by the asymptotic...

A branching random field with immigration is considered. The demographic variation process is a non-Markovian signed measure-valued process which measures the changes in the system due to branchings and deaths in the population. The asymptotic behavior of this process under various scalings is...

In this paper we consider the class C of test statistics T = [Sigma]j = 1p Q(lj) for testing the multivarite linear hypothesis and independence of two sets of variables. Here Q(l) is a monotone increasing function for l = 0, Q(0) = 0, Q'(0) = 1, and has a continuous third order derivative in a...

This paper introduces a family of multivariate symmetric distributions, which includes the one with i.i.d. exponential components as its special member. This family, denoted by Fn, is defined as scale mixtures of the uniform distribution on the surface of the l1 unit sphere and studied from...

Suppose that independent observations come from an unspecified unknown distribution. Then we consider the maximum likelihood based on a specified parametric family which provides a good approximation of the true distribution. We examine the asymptotic properties of the maximum likelihood...

Recently, numerous practical applications of multivariate Gaussian Markov random fields (GMRF) on a lattice have emerged. However, the theory is not satisfactorily developed. We give various properties of multivariate GMRF for multi-dimensional lattice. In particular, some multivariate MRF are...

For each positive integer n = 1, let Z2n be the direct product of n copies of Z2, i.e., Z2n = {(a1, a2, ..., an)[short parallel]ai = 0 or 1 for all I = 1, 2, ..., n} and let {Wtn}t=0 be a random walk on Z2n such that P{W0n = A} = 2-n for all A's in Z2n and for all j = 0, 1, 2, ..., and all (a1,...