Institute of Mathematical Statistics Lecture Notes - Monograph Series

Recent developments towards optimality in multiple hypothesis testing

Juliet Popper Shaffer

Full-text: Open access


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.

Chapter information

Javier Rojo, ed., Optimality: The Second Erich L. Lehmann Symposium (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 16-32

First available in Project Euclid: 28 November 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J15: Paired and multiple comparisons
Secondary: 62C25: Compound decision problems 62C20: Minimax procedures

power familywise error rate false discovery rate directional inference Types I, II and III errors

Copyright © 2006, Institute of Mathematical Statistics


Shaffer, Juliet Popper. Recent developments towards optimality in multiple hypothesis testing. Optimality, 16--32, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000374.

Export citation