In this paper recent results of [6]Ann. Statist.5 110-123] are used to obtain the asymptotic null distribution of a weighted Cramér-von Mises type test for independence. We use approximate Bahadur slopes to find good weight functions for certain alternatives. Some percentage points of the...

Let X be a Gaussian rv with values in a separable Hilbert space H having a covariance operator R of the form R = L0*A*AL0, where L0, A are linear operators on H. A method is given for computing in terms of R0 = L0*L0 and A the distribution of X2, · being the norm in H. The result is applied...

Some fundamental properties of the empirical distribution functions are derived in the case of mixing random variables. These properties are then utilized to study asymptotic normality and strong laws of large numbers for functions of order statistics.

Let Y be an N([mu], [Sigma]) random variable on Rm, 1 <= m <= [infinity], where [Sigma] is positive definite. Let C be a nonempty convex set in Rm with closure . Let (·,-·) be the Eculidean inner product on Rm, and let [mu]c be the conditional expected value of Y given Y [set membership, variant] C. For v [set membership, variant] Rm and s >= 0, let [beta]s(v) be the expected value of (v, Y) - (v, [mu])s and let [gamma]s(v) be the conditional expected value of (v, Y) - (v, [mu]c)s given Y [set membership, variant] C. For s = 1, [gamma]s(v) [beta]s(v) if and only if , and...</=>

The empirical characteristic function is considered as a tool for large sample testing of a hypothesis that can be characterized in terms of the characteristic function. Two test statistics based upon the empirical characteristic function are proposed. The limiting distributions of these test...

In this paper, some of the familiar transformations of r are examined for their robustness to nonnormality. General results are given for any parent population f(x, y) and any general transformation g(r) of r. Two types of parent populations are considered for exemplification: The bivariate...

Sharpe has shown that full operator-stable distributions [mu] on Rn are infinitely divisible and for a suitable automorphism B depending on [mu] satisfy the relation [mu]t = [mu]t-B * [delta](b(t)) for all t 0. B is called an exponent for [mu]. It is proved here that if an operator-stable...

The probability measure of X = (x0,..., xr), where x0,..., xr are independent isotropic random points in n (1 = r = n - 1) with absolutely continuous distributions is, for a certain class of distributions of X, expressed as a product measure involving as factors the joint probability measure of...

We prove that integrability of the norm is the best sufficient condition in terms of integrability of functions of the norm for a positive measure to be a Lévy Measure in C[0, 1].

In recent years, applications of cohomology theory to some aspects of probability theory have been found useful. In this paper, such applications are discussed for a determination of infinitely divisible positive definite functions on topological groups. This theory can be viewed as a new method...