The positivity of the best linear unbiased estimator of the scale parameter of a location-scale family of distributions in terms of complete or selected set of order statistics has only been conjectured in the literature based solely on empirical evidence. This paper offers an analytical proof...

Considering independent test statistics, Simes' critical values are modified and newer sets of critical values, each providing an exact control of the type I error rate, are obtained. These modifications, as simulations show, quite often yield more powerful tests than the original Simes' test.

A multivariate extension of Cohen's (1972, J. Amer. Statist. Assoc. 67 382-387) result on interval estimation of normal variance is made in this article. Based on independent random matrices X : p - m and S : p - p distributed, respectively, as Npm([mu], [Sigma] [circle times operator] Im) and...

Sarkar (1998) showed that certain positively dependent (MTP2) random variables satisfy the Simes inequality. The multivariate-t distribution does not satisfy this (MTP2) property, so other means are necessary. A corollary was given in Sarkar (1998) to handle this distribution, but there is an...

In this paper we introduce a sequence of inequalities for a joint probability of equicoordinate, one-sided rectangles of higher dimension based on joint probabilities of lower dimension, and show that the resulting lower and upper bounds hold for certain cases of equicorrelated multivariate...

Testing multiple null hypotheses in two stages to decide which of these can be rejected or accepted at the first stage and which should be followed up for further testing having had additional observations is of importance in many scientific studies. We develop two procedures, each with two...