STATS 300 C Homework 3

1 In multiple testing, weighted procedures are used for various reasons; for instance, (1) to increase power, (2) to incorporate previous knowledge about individual hypotheses, (3) to represent difference in importance (some hypotheses may be more important than others) or (4) to incorporate other measures of loss. The purpose of this question is to examine weighted procedures. Here, we assume that we have m-hypotheses H1, . . . ,Hm with p-values p1, . . . , pm. As usual, the p-values corresponding to true nulls are assumed to be uniformly distributed.