For a given score function [psi] = [psi](x, [theta]), let [theta]n be Huber's M-estimator for an unknown population parameter [theta]. Under some mild smoothness assumptions it is known that n1/2([theta]n - [theta]) is asymptotically normal. In this paper the stopping times [tau]c(m) = inf{n =...

In this paper, the authors considered various procedures for testing for the independence of two multivariate regression equations with different design matrices. Asymptotic null distributions as well as nonnull distributions under local alternatives of the test statistics associated with the...

This is an expository paper. The derivation of the ordinary central limit theorem using the Fourier transform on the real line is reviewed. Harmonic analysis on the Poincaré-Lobatchevsky upper half plane H is sketched. The Fourier inversion formula on H reduces to that for the classical...

The following estimate of the pth derivative of a probability density function is examined: [Sigma]k = 0Nâkhk(x), where hk is the kth Hermite function and âk = ((-1)p/n)[Sigma]i = 1n hk(p)(Xi) is calculated from a sequence X1,..., Xn of independent random variables having the common unknown...

Xt is a Brownian sheet defined for t belonging to the positive orthant of RN, for which the covariance function is given by E(XsXt = [Pi]i = 1N min(si,ti). Functions [phi] with suitable growth conditions are classified as lower or upper class near the origin according as Xt does or does not...

Let {vij} i,j = 1, 2,..., be i.i.d. standardized random variables. For each n, let Vn = (vij) I = 1, 2,..., n; J = 1, 2,..., S = s(n), where (n/s) -- y 0 as n -- [infinity], and let Mn = (1/s)VnVnT. Previous results [7, 8] have shown the eigenvectors of Mn to display behavior, for n large,...

A construction of the Hellinger square integral with respect to a semispectral measure in a Banach space B is given. It is proved that the space of values of a B-valued stationary stochastic process is unitarily isomorphic to the space of all B*-valued measures that are Hellinger square...

We find sufficient conditions for the equivalence of two measures on function space induced by infinitely divisible processes. The processes are not assumed to be stochastically continuous or to have independent increments. The theorem proved here is equivalent to known results in the special...

Let Z = {Z0, Z1, Z2,...} be a martingale, with difference sequence X0 = Z0, Xi = Zi - Zi - 1, i = 1. The principal purpose of this paper is to prove that the best constant in the inequality [lambda]P(supi Xi = [lambda]) <= C supiE Zi, for [lambda] > 0, is C = (log 2)-1. If Z is finite of length n, it is proved that the best...</=>

A stability result for sums of weighted nonnegative random variables is established and then it is utilized to obtain, among other things, a slight generalization of the Borel-Cantelli lemma and to show that the work of Jamison, Orey, and Pruitt (Z. Wahrsch. Verw. Gebiete 4 (1965), 40-44) on...