Data Volume and Power of Multiple Tests with Small Sample Size Per Null

Zhiyi Chi

Communications in Statistics - Theory and Methods, 2009, vol. 38, issue 16-17, 2784-2803

Abstract: In multiple hypothesis testing, the volume of data, defined as the number of replications per null times the total number of nulls, usually defines the amount of resource required. On the other hand, power is an important measure of performance for multiple testing. Due to practical constraints, the number of replications per null may not be large enough. For the case where the population fraction of false nulls is constant, we show that, as the difference between false and true nulls becomes increasingly subtle while the number of replications per null cannot increase fast enough: (1) in order to have enough chance that the data to be collected will yield some trustworthy findings, as measured by a conditional version of the positive false discovery rate (pFDR), the volume of data has to grow at a rate much faster than in the case where the number of replications per null can be large enough; and (2) in order to control the pFDR asymptotically, power has to decay to 0 in a rate highly sensitive to rejection criterion and there is no asymptotically most powerful procedures among those that control the pFDR asymptotically at the same level.

Date: 2009
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610910902936349 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:38:y:2009:i:16-17:p:2784-2803

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610910902936349

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().