Consider an r - c contingency table under the full multinomial model where each category is ordered. The problem is to test the null hypothesis of independence against the alternative that all local log odds ratios are nonnegative with a least one local log odds ratio positive. We find the class...

It is shown that the conditional probability density function of Y1 given (1/n) [Sigma]i=1n Yi=1Yit = [Sigma], where Y1, Y2,..., Yn are i.i.d, p-variate uniform random vectors with mean 0 equals to that of Y1 given (1/n) [Sigma]i=1n YiYit,..., Yn are i.i.d, p-variate normal random vectors with...

Nonuniform convergence rates in the central limit theorem for martingale difference arrays are derived. The main result is for bounded variables, and a consequence is a sharp estimate with only two moments.

For weighted sums [Sigma]j = 1najVj of independent random elements {Vn, n = 1} in real separable, Rademacher type p (1 <= p <= 2) Banach spaces, a general weak law of large numbers of the form ([Sigma]j = 1najVj - vn)/bn -->p 0 is established, where {vn, n = 1} and bn -- [infinity] are suitable sequences. It is assumed that {Vn, n = 1} is stochastically dominated by a random element V, and the...</=>

It is given a uniform estimate of the rate of convergence in CLT on stratified groups for variational distance when some pseudomoment is sufficiently small. Moreover, it is given a nonuniform estimate on the system of homogeneous balls when some pseudomoment is finite.

We consider an estimation problem with observations from a Gaussian process. The problem arises from a stochastic process modeling of computer experiments proposed recently by Sacks, Schiller, and Welch. By establishing various representations and approximations to the corresponding...

The excess-mass ellipsoid is the ellipsoid that maximizes the difference between its probability content and a constant multiple of its volume, over all ellipsoids. When an empirical distribution determines the probability content, the sample excess-mass ellipsoid is a random set that can be...

We present a method for proving finite versions of De Finetti-type theorems for general measurable spaces (). Bernstein operators on the one dimensional simplex [0, 1] are generalized to Bernstein operators on limits of simplices, representing distributions on (). The positivity of finite moment...

It has been shown ([6], Ph.D. dissertation, Harvard University) that the remainder term of a form of the Taylor expansion, involving Hadamard derivative, of the statistical functional is asymptotically negligible. This result is extended to a more general form with respect to weighted empirical...

Let Vk,m denote the Stiefel manifold which consists of m - k(m = k) matrices X such that X'X = Ik. Let X1,..., Xn be a random sample of size n from the matrix Langevin (or von Mises-Fisher) distribution on Vk,m, which has the density proportional to exp(tr F'X), with F an m - k matrix, and let Z...