Recent developments towards optimality in multiple hypothesis testing

Details Recent developments towards optimality in multiple hypothesis testing Recent developments towards optimality in multiple hypothesis testing

2006-10-27

arxiv.org/abs/math/0610841v1

IMS Lecture Notes--Monograph Series 2006, Vol. 49, 16-32

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/074921706000000374 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

10.1214/074921706000000374

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.

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