Recent developments towards optimality in multiple hypothesis testing

Abstract

There are many different notions of optimality even in testing a single hypothesis. In the multiple testing area, the number of possibilities is very much greater. The paper first will describe multiplicity issues that arise in tests involving a single parameter, and will describe a new optimality result in that context. Although the example given is of minimal practical importance, it illustrates the crucial dependence of optimality on the precise specification of the testing problem. The paper then will discuss the types of expanded optimality criteria that are being considered when hypotheses involve multiple parameters, will note a few new optimality results, and will give selected theoretical references relevant to optimality considerations under these expanded criteria.

Published at http://dx.doi.org/10.1214/074921706000000374 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (6)

• Generalizations of the Familywise Error Rate
• Estimating the proportion of false null hypotheses among a large number of independently tested hypotheses
• Decision theory results for one-sided multiple comparison procedures
• On Optimality of Stepdown and Stepup Multiple Test Procedures
• Characterization of Bayes procedures for multiple endpoint problems and inadmissibility of the step-up procedure
• On likelihood ratio tests