In the paper the problem of nonnegative estimation of [beta]'H[beta] + h[sigma]2 in the linear model E(y) = X[beta], Var(y)= [sigma]2I is discussed. Here H is a nonnegative definite matrix while h is a nonnegative scalar. An iterative procedure for the nonnegative minimum biased quadratic...

Let (X, X; [set membership, variant] d} be a field of independent identically distributed real random variables, 0 < p < 2, and {a,; (, ) [set membership, variant] d - d, <= } a triangular array of real numbers, where d is the d-dimensional lattice. Under the minimal condition that sup, a, < [infinity], we show that - 1/p [summation operator] <= a, X --> 0 a.s. as -- [infinity] if and only if E(Xp(LX)d - 1) < [infinity] provided d >= 2. In the above, if 1 = p 2, the random variables are needed to be centered at the mean. By establishing a certain law of...</[infinity]></p>

Let Z be a random vector following the p-variate normal distribution N(0, Ip), and let S be a positive definite random matrix independent of Z. The probability density function f(x) of the random vector X = S1/2Z is expanded around that of N(0, Ip) and its error bound is evaluated in terms of...

Suppose that Y is distributed as multivariate normal with unknown covariance matrix and that N independent observations are available on Y. An important special case of the problem studied in this paper is that of testing the null hypothesis that the mean of Y is zero against the alternative...

Cone order association, which generalizes the notion of association, is defined. For cone order association, functions which are nondecreasing with respect to a cone order, are nonnegatively correlated. Properties and sufficient conditions are developed. The main result yields a necessary and...

We study a method for estimating a density f in Rd under assumptions which are of qualitative nature. The resulting density estimator can be considered as a generalization of the Grenander estimator for monotone densities. The assumptions on f are given in terms of shape restrictions of the...

The principal components of a vector of random variables are related to the common factors of a factor analysis model for this vector. Conditions are presented under which components and factors as well as factor proxies come close to each other. A similar analysis is carried out for the...

We develop some examples of degenerate U-statistic tests for uniformity in certain compact topological groups and homogeneous spaces, namely, the orthogonal group and the Grassmann manifold. These tests have the attractive properties that they involve simple matrix calculations and their...

An asymptotic theory is developed for the estimation of high quantile curves, i.e., sets of points in higher dimensional space for which the exeedance probability is pn, with npn -- 0 (n -- [infinity]). Here n is the number of available observations. This is the situation of interest if one...

We consider estimation of a multivariate probability density function f(x) by kernel type nearest neighbor (nn) estimators gn(x). The development of nn density estimation theory has had a rich history since Loftsgaarden and Quesenberry proposed the idea in 1965. In particular, there is a vast...