A class of local correlation functions is obtained from B-spline bases and the corresponding stationary processes are constructed through local integration. Then a local Bayes estimate (LBE) is proposed using this process as a prior in a signal estimation problem. Mean square convergence of this...

When Z is a random L2H-valued measure, where H is a Hilbert space, we prove that there exists an L2q-valued measure, which may depend on constraints and which best sums up the random measure Z according to a stationary criterion. Then a technique to reduce a random function is deduced from the...

We define the appropriate analogue of Student's t-statistic for multivariate data, and prove that it is asymptotically normal for random vectors in the domain of attraction of the normal law. We also prove that Hotelling's T2-statistic has a chi-squared limiting distribution for random vectors...

This paper deals with the problem of classifying a multivariate observation X into one of two populations [Pi]1: p(x; w(1)) [set membership, variant] S and [Pi]2: p(x; w(2)) [set membership, variant] S, where S is an exponential family of distributions and w(1) and w(2) are unknown parameters....

We consider some tests to detect a change-point in a multiple linear regression model. The tests are based on the maxima of the weighted cumulative sums processes. The limit distributions may be double exponential or maxima of Gaussian processes depending on the set where the maximum of the...

Let 1n be an estimator of an IFRA survival function 1 and let A be such that 0 < 1(A) < 1. The main result constructs an IFRA estimator by splicing the smallest increasing failure rate on the average majorant and greatest increasing failure rate on the average minorant of the restrictions of 1n to the intervals [0, A] and [A, [infinity]), respectively. The resulting etimator 1n has the property that supx 1n - 1 <= k supx 1n - 1 where k >= 2, and k = 2 if and only if A is the median of F. As a consequence, if 1n represents the empirical survival function, or the Kaplan-Meier estimator, the estimator 1n inherits the strong and uniform convergence...</1(a)>

Let Xn, n = 1, 2, ... be a sequence of p - q random matrices, p = q. Assume that for a fixed p - q matrix B and a sequence of constants bn -- [infinity], the random matrix bn(Xn - B) converges in distribution to Z. Let [psi](Xn) denote the q-vector of singular values of Xn. Under these...

We consider the convergence of adaptive direction sampling, concentrating mainly on a special case, the "snooker algorithm" for which a powerful irreducibility result can be proved under extremely mild regularity conditions.

The bivariate normal distribution function is approximated with emphasis on situations where the correlation coefficient is large. The high accuracy of the approximation is illustrated by numerical examples. Moreover, exact upper and lower bounds are presented as well as asymptotic results on...

In this paper, several properties of the multivariate Pareto (IV) distribution introduced by B. C. Arnold (Pareto Distributions, International Cooperative Publ. House, FairIand, MD) are studied. It is shown that in the multivariate Pareto (IV), if all the inequality parameters are the same, then...