Necessary and sufficient conditions for an arbitrary q-variate stationary sequence xt, t [set membership, variant] , to be deterministic are presented. A characterization of the rank r(x) of xt, t [set membership, variant] , and a method to construct the Wold-Cramér decomposition for xt, t [set...

We consider estimation of the parameter B in a multivariate linear functional relationship Xi=[xi]i+[xi]1i, Yi=B[xi]i+[xi]2i, i=1,...,n, where the errors ([zeta]1i', [zeta]2i') are independent standard normal and ([xi]i, i [set membership, variant] ) is a sequence of unknown nonrandom vectors...

Martingale theory is used to obtain a central limit theorem for degenerate U-statistics with variable kernels, which is applied to derive central limit theorems for the integrated square error of multivariate nonparametric density estimators. Previous approaches to this problem have employed...

We give almost sure convergence of appropriately normalized particle numbers in bounded domains of locally supercritical branching diffusion processes with one-dimensional periodic diffusions as their non-branching part processes. Some spectral properties of periodic diffusion operators...

The strong consistency of M-estimators in linear models is considered. Under some conditions on the ratios of maximum and minimum eigenvalues of the information matrices the desired result is established.

A bivariate Gaussian process with mean 0 and covariance is observed in some region [Omega] of R', where {[Sigma]ij(s,t)} are given functions and p an unknown parameter. A test of H0: P = 0, locally equivalent to the likelihood ratio test, is given for the case when [Omega] consists of p points....

For fixed p (0 <= p <= 1), let {L0, R0} = {0, 1} and X1 be a uniform random variable over {L0, R0}. With probability p let {L1, R1} = {L0, X1} or = {X1, R0} according as ; with probability 1 - p let {L1, R1} = {X1, R0} or = {L0, X1} according as , and let X2 be a uniform random variable over {L1, R1}. For n >= 2, with probability p let {Ln, Rn} = {Ln - 1, Xn} or = {Xn, Rn - 1} according as , with probability 1 - p let {Ln, Rn} = {Xn, Rn - 1} or = {Ln - 1, Xn} according as , and let Xn + 1 be a uniform random variable over {Ln, Rn}. By this iterated procedure, a random sequence {Xn}n =...</=>

One and two sample rank statistics are shown in general to be more efficient in the Bahadur sense than their sequential rank statistic analogues as defined by Mason (1981, Ann. Statist.9 424-436) and Lombard (1981, South African Statist. J.15 129-152), even though the two families of statistics...

Fairly general sufficient conditions are given to guarantee that invariant tests about means in the multivariate linear model and the repeated measures model have the correct asymptotic size when the normal assumption under which the tests are derived is relaxed. These conditions are the same as...

The concept of a quasimartingale, and therefore also of a function of bounded variation, is extended to processes with a regular partially ordered index set V and with values in a Banach space. We show that quasimartingales can be described by their associated measures, defined on an inverse...