This article studies the strong consistency of M-estimates in linear regression models directly from the minimization problem 75, where X1. X2, ... can be random observations of a p-dimensional random vector X, or that they are simply known nonrandom p-vectors. It is shown that the solution...

A notion of association of probability measures on partially ordered (Polish) spaces is introduced and its basic properties are investigated. This generalizes the classical notion of association among random variables, due to Esary, Proschan, and Walkup. The relation between association and...

Let {vij; i, J = 1, 2, ...} be a family of i.i.d. random variables with E(v114) = [infinity]. For positive integers p, n with p = p(n) and p/n -- y 0 as n -- [infinity], let Mn = (1/n) Vn VnT , where Vn = (vij)1 = i = p, 1 = j = n, and let [lambda]max(n) denote the largest eigenvalue of Mn. It...

A general solution of the Deny convolution equation restricted to a half line is obtained using certain concepts of random walk theory. The equation in question arises in several places in applied probability such as in queueing and storage theories and characterization problems of probability...

The equivalence of sequences of probability measures jointly with the extension of Skorohod's representation theorem due to Blackwell and Dubins is used to obtain strong convergence of weighted sums of random elements in a separable Banach space. Our results include most of the known work on...

In a recent paper Subba Rao and Gabr (J. Time Ser. Anal. (1987), in press) considered the estimation of the spectrum and the inverse spectrum based on the method by Pisarenko (Geophys. J. Roy. Astronom. Soc. 28 (1972), 511-531). The asymptotic properties of these estimates were studied using the...

A bias-adjusted maximum likelihood estimator (mle), which has been shown to possess certain optimality criteria as an estimate of [theta] (see Ghosh, J. K., Sinha, B. K., and Joshi, S. N. (1982). In Statistical Decision Theory and Related Topics III (S. S. Gupta and J. O. Berger, Eds.), Vol. 1,...

The set of all bivariate probability distributions with support contained in {(i,j); I=1, 2 and J = 1,2,...,n} which are totally positive of order two is shown to be a convex set under some conditions on one of the marginal distributions. The extreme points of this compact convex set are...

The joint asymptotic distributions of the marginal quantiles and quantile functions in samples from a p-variate population are derived. Of particular interest is the joint asymptotic distribution of the marginal sample medians, on the basis of which tests of significance for population medians...

Asymptotic properties for censored data with staggered entry are studied in a parametric counting process model. In particular, we get the weak convergence of the score process and the MLE process and the local asymptotic normality (LAN) for this parametric family, all treated in D[0,...