Let X1, X2 ,..., Xp be p random variables with joint distribution function F(x1 ,..., xp). Let Z = min(X1, X2 ,..., Xp) and I = i if Z = Xi. In this paper the problem of identifying the distribution function F(x1 ,..., xp), given the distribution Z or that of the identified minimum (Z, I), has...

Let R(s, t) be a continuous, nonnegative, real valued function on a <= s <= t <= b. Suppose [not partial differential]R/[not partial differential]s >= 0, [not partial differential]R/[not partial differential]t = 0, and [not partial differential]2R/[not partial differential]t [not partial differential]t = 0 in the interior of the domain. Then the extension of R to a symmetric...</=>

The class of general incomplete multiresponse (randomized block) models, in which it is not necessary for all responses to be measured on every experimental unit, is considered. For p = 2 responses, the optimum model is obtained under a reasonable cost constraint and the determinant criterion....

Let X be a (real) separable Banach space, let {Vk} be a sequence of random elements in X, and let {ank} be a double array of real numbers such that limn--[infinity] ank = 0 for all k and [Sigma][infinity]k=1 ank = 1 for all n. Define Sn = [Sigma]nk=1 ank(Vk - EVk). The convergence of {Sn} to...

The exact null distribution of the likelihood ratio criterion for testing H0: [Sigma] = [Sigma]0 and [mu] = [mu]0 against alternatives H1: [Sigma] [not equal to] [Sigma]0 or [mu] [not equal to] [mu]0 in Np([mu], [Sigma]) has been obtained as (a) a chi-square series and (b) a beta series....

The rates of convergence of the distribution function of quadratic rank statistics to the X2-distribution under hypothesis and near alternatives are investigated. The considered quadratic rank statistics are used for testing the multivariate hypothesis of randomness. The method suggested by...

The paper deals with optimal quadratic unbiased estimation of the unknown dispersion matrix in multivariate regression models without assuming normality of the errors. We show that Hsu's theorem for univariate regression models continues to multivariate models with no additional assumptions....

In this paper, the authors derived exact central distributions of the extreme roots of the Wishart and MANOVA matrices. The expressions for these distributions and the associated probability integrals are written as linear combinations of the products of certain double integrals. The double...

Tamhankar [2] showed that, under suitable conditions, if X1, ..., Xn are independent random variables, then they are normally distributed with zero means and equal variances if and only if R is independent of ([Theta]1, ..., [Theta]n-1), R and [Theta]1, ..., [Theta]n-1 being the corresponding...

In this note we obtain rates of convergence in the central limit theorem for certain maximum of coordinate partial sums of independent identically distributed random vectors having positive mean vector and a nonsingular correlation matrix. The results obtained are in terms of rates of...