Peter H. Westfall Which Multiple Testing Methods are Optimal?
Texas Tech University
Decision theory provides answers.
* While FDR-controlling methods are optimal for certain kinds of loss
functions, the Bonferroni method is optimal for others.
* For additive loss, correlation between test statistics does not affect
expected loss, but quantiles of loss are affected by correlations.
* The choice of additive loss is made for mathematical convenience. The
practical validity of additive loss is questionable; reasonable
non-additive loss functions provide different optimal tests.
* Point-null multiple hypothesis testing methods have increased loss as n
increases. Methods based on empirical nulls do not.