The main result of this paper is summarized in Theorem 1, which states that when certain conditions of a general nature are satisfied, the data-based histogram density estimator is strongly consistent in the sence that the mean absolute derivation of the estimator and the density function...

Strictly operator-stable distributions are defined and discussed. Characterization of strictly stable distributions with exponent 1 is generalized to strictly ([alpha], Q)-stable distributions with [alpha] being an eigenvalue of Q.

Consider the problem of testing a simple hypothesis that [theta] = 0 against the alternative that [theta] [not equal to] 0. This paper makes an asymptotic comparison (up to o(n-1)) between Rao's test and the locally most powerful unbiased (LMPU) test under contiguous alternatives, [delta]n-1/2,...

The individuals of a population reproduce according to a linear birth process and simultaneously and independently diffuse inp-dimensional Euclidean space according to a Brownian process with dependent coordinates. The properties of the maximum likelihood estimators of the drift vector and the...

The theory of compact group actions on locally compact abelian groups provides a unifying theory under which different invariance conditions studied in several contexts by a number of statisticians are subsumed as special cases. For example, Schoenberg's characterization of radially symmetric...

A new series representation of the exact distribution of Hotelling's generalized T02 statistic is obtained. Unlike earlier work, the series representation given here is everywhere convergent. Explicit formulae are given for both the null and the non-central distributions. Earlier results by [1],...

In the univariate case it is well known that the one sided t test is uniformly most powerful for the null hypothesis against all one sided alternatives. Such a property does not easily extend to the multivariate case. In this paper, a test derived for the hypothesis that the mean of a vector...

Let {Xt} be a Gaussian ARMA process with spectral density f[theta]([lambda]), where [theta] is an unknown parameter. To estimate [theta] we propose a minimum contrast estimation method which includes the maximum likelihood method and the quasi-maximum likelihood method as special cases. Let...

We introduce the notion of semistable processes and semistable random measures; and give a characterization of semistable laws on Banach spaces. Using this charcterization, we discuss the existence of semistable random measures, define the stochastic integrals with respect to these measures, and...

We give general conditions for extremality and the global Markov property of Gibbs measures for an attractive Markov specification. As a special case we prove the global Markov property for the FKG-maximal Gibbs measures [mu]±, which give models of Euclidean Field Theory on the lattice.