Let {X(t), 0 = t = T} and {Y(t), 0 = t = T} be two additive processes over the interval [0, T] which, as measures over D[0, T], are absolutely continuous with respect to each other. Let [mu]X and [mu]Y be the measures over D[0, T] determined by the two processes. The characteristic function of...

Using the concepts of conditional expectation and independence of subalgebras, we characterize those contractive projections, P, on Lp, over a probability measure space, having the property that I - P is contractive. By contractive projection we mean a linear operator, P, on the Lebesgue space,...

Given three independent multivariate samples, of which, two are from unknown populations that are known to be distinct and the other is from an unknown mixture of the two, the problem of estimation of the mixture rate is considered. A procedure based on linearly compounded rank-scores is studied...

In this paper we deal with the problem of classifying a multiresponse observation into one of two p-variate normal populations with unknown mean vectors and a known and common dispersion matrix. The classification procedure is based on two general incomplete multiresponse samples (i.e., not all...

It is shown here that Bahadur's [Ann. Math. Statist. (1966) 37, 577-580] almost sure (a.s.) asymptotic representation of a sample quantile for independent and identically distributed random variables holds under certain regularity conditions for a general class of stationary multivariate...

Let ([Omega], , [mu]) be a measure space, a separable Banach space, and * the space of all bounded conjugate linear functionals on . Let f be a weak* summable positive B(*)-valued function defined on [Omega]. The existence of a separable Hilbert space , a weakly measurable B()-valued function Q...

We call a set of univariate distributions with the same mathematical form but different parameter values a family . Consider a bivariate Gumbel Type A survival distribution, S12(x1, x2), defined in (2.1), for which both marginal distributions, S1(x1), S2(x2), belong to the same family, of...

Let [mu] be the mean function of an observable stochastic process whose sample paths fall in some Banach space with a basis and assume [mu] is also in this space. A procedure like Cover's (Ann. Statist.1, 862-871, 1973) is given which has the property that if the last nonzero coordinate of [mu]...

A general method for obtaining inequalities of Cramér-Rao type for convex loss functions is presented. It is shown under rather weak assumptions that there are at least as many such inequalities as best unbiased estimators. More precisely, it is shown that an estimator is efficient with respect...

The aim of this article is to give an axiomatic characterization of the multivariate measure of "affinity" among a number of distributions. This measure has been used in the last few years for statistical decision making. When there are only two distributions involved this measure of affinity is...