In an exponential family of distributions, the problem of testing for homogeneity of a set of parameters against some restricted alternatives is considered. Incorporating Roy's union-intersection (UI) principle, Rao's efficient score test is extended to such restricted alternatives, and is shown...

A general distribution which will be called the noncentral generalized Laplacian (NGL) is introduced and its properties studied. Then a set of results are obtained which will give the necessary and sufficient conditions for a bilinear expression or a quadratic expression to be distributed as a NGL.

Motivated by recent work on exploratory projection pursuit, we define the empirical Radon transform. Its precise convergence rate at a fixed centre, uniform over all orientations, and its precise convergence rate uniformly over all centres and all orientations are derived. We show that in the...

We consider the first-order Edgeworth expansion for summands related to a homogeneous Markov chain. Certain inaccuracies in some earlier results by Nagaev are corrected and the expansion is obtained under relaxed conditions. An application of our result to the distribution of the mle of a...

Consider the model where Xij, i = 1, ..., k; j = 1, 2, ..., ni are observed. Here Xij are independent N([theta]i, [sigma]2). Let [theta]' = ([theta]1, ..., [theta]k) and let A1 be a (k - m) - k matrix of rank (k - m), 0 <= m <= k - 1. The problem is to test H: A1[theta] = 0 vs K - H where K: A1[theta] >= 0. A wide variety of order restricted alternative problems are included in...</=>

Parametric families of continuous bivariate distributions with given margins that include independence and perfect positive dependence are compared on the basis on some important properties. Since many such families exist, the comparisons are helpful for deciding on suitable models for...

Multivariate stable densities do not generally have explicit formula, but they can be specified indirectly by means of a spectral measure. Our main result gives an approximation that is used for numerical computation of these densities. We construct a discrete spectral measure, with explicit...

Denoting by X(1) <= X(2) <= · · · <= X(n) the order statistic based on a random sample X1, X2, ..., Xn drawn from a distribution F, it is shown that the property "E(X1X(1), X(n)) = (X(1) + X(n)), almost surely" holds for some n >= 3 if and only if F is either a uniform distribution on an interval or a discrete uniform distribution supported on a set of equispaced points. The heart of our proof is the interesting observation that the above equation involving conditional expectations completely determines...</=>

We develop mathematical models for high-dimensional binary distributions, and apply them to the study of smoothing methods for sparse binary data. Specifically, we treat the kernel-type estimator developed by Aitchison and Aitken (Biometrika63 (1976), 413-420). Our analysis is of an asymptotic...

When a multivariate elliptical distribution is used as the basis in multivariate analysis all fourth-order cumulants are expressed in terms of a single kurtosis parameter. This and other well-known properties place unrealistic restrictions on the distribution of the covariance matrix. In this...