P. Masani and the author have previously answered the question, "When is an operator on a Hilbert space the integral of a complex-valued function with respect to a given spectral (projection-valued) measure?" In this paper answers are given to the question, "When is a linear operator from q to p...

This paper investigates the characterizations of certain discrete distributions within the framework of a multivariate additive damage model. The univariate case for such a model appeared in an article by [2]. In this model a p-dimensional observation is subjected to damage according to a...

The concept of a semi-martingale is extended to processes with index set in the plane. The definitions of planar semi-martingales are similar to those of two parameter bounded variation. Necessary and sufficient conditions for a Doob-Meyer decomposition are obtained, and a maximal inequality and...

Let Xj (j = 1,...,n) be i.i.d. random variables, and let Y' = (Y1,...,Ym) and X' = (X1,...,Xn) be independently distributed, and A = (ajk) be an n - n random coefficient matrix with ajk = ajk(Y) for j, K = 1,...,n. Consider the equation U = AX, Kingman and Graybill [Ann. Math. Statist. 41...

Mean estimation for a random function is considered in its most general context, including both the case of infinite dimensional mean and exact estimation. The existence theorem for the best linear unbiased estimates is established. The general definition of the pseudobest estimate is given;...

Separation theorems for singular values of a matrix, similar to the Poincaré separation theorem for the eigenvalues of a Hermitian matrix, are proved. The results are applied to problems in approximating a given r.v. by an r.v. in a specified class. In particular, problems of canonical...

Based on a random sample from a population with (unknown) probability density f, this note exhibits a class of statistics f(p) for each fixed integer p [greater, double equals] 0. It is shown that f(p) are uniformly strongly consistent estimators of f(p), the pth order derivative of f, if and...

Two extensions of the T-method for multiple comparisons on a set of parameters are discussed, which are easily applied to cases where the allied random variables do not satisfy the usual conditions imposed by the T-method. The two generalized T-procedures are compared with the S and the...

A simple branching diffusion process is given as an elementary model of spatial evolution. A parametric estimation theory is presented for this model. As side results, a spatial central limit theorem and spatial strong law of large numbers are also obtained.

Under appropriate assumptions, expressions describing the asymptotic behavior of the bias and variance of k-nearest neighbor density estimates with weight function w are obtained. The behavior of these estimates is compared with that of kernel estimates. Particular attention is paid to the...