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...

For testing multiple null hypotheses, the classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of even one false rejection. In many applications, one might be willing to tolerate more...

It is a common practice to use resampling methods such as the bootstrap for calculating the p-value for each test when performing large scale multiple testing. The precision of the bootstrap p-values and that of the false discovery rate (FDR) relies on the number of bootstraps used for testing...

Hochberg & Benjamini (1990) first presented adaptive procedures for controlling familywise error rate. However, until now, it has not been proved that these procedures control the familywise error rate. We introduce a simplified version of Hochberg & Benjamini's adaptive Bonferroni and Holm...

The Benjamini-Hochberg step-up procedure controls the false discovery rate (FDR) provided the test statistics have a certain positive regression dependency. We show that this procedure controls the FDR under a weaker property and is optimal in the sense that its critical constants are uniformly...

Formulas for covariance matrix between a random vector and its ordered components are derived for different distributions including multivariate normal,t, andF. The present formulas and related results obtained here lead to some known results in the literature as special cases.

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.

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...