STATS 300 C Homework 3
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چکیده
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.
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Stats 300 C : Theory of
We have seen that the BH procedure controls the FDR for multiple testing when the p-values are independent. How can we control the FDR under dependence? Here, we consider the case where the statistics have distribution Y ∼ N (μ,Σ); in the past, we have assumed that Σ = Ip. If the covariance matrix Σ were known, we could reduce to the independent case using the transformation Y ′ = Σ− 1 2Y , so ...
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