Optimal testing of equivalence hypotheses
成果类型：
Article
署名作者：
Romano, JP
署名单位：
Stanford University
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/009053605000000048
发表日期：
2005
页码：
1036-1047
关键词：
摘要：
In this paper we consider the construction of optimal tests of equivalence hypotheses. Specifically, assume X-1,..., X-n are i.i.d. with distribution P theta, with theta is an element of R-k. Let g(theta) be some real-valued parameter of interest. The null hypothesis asserts g(theta) is an element of (a, b) versus the alternative g(theta) is an element of (a, b). For example, such hypotheses occur in bioequivalence studies where one may wish to show two drugs, a brand name and a proposed generic version, have the same therapeutic effect. Little optimal theory is available for such testing problems, and it is the purpose of this paper to provide an asymptotic optimality theory. Thus, we provide asymptotic upper bounds for what is achievable, as well as asymptotically uniformly most powerful test constructions that attain the bounds. The asymptotic theory is based on Le Cam's notion of asymptotically normal experiments. In order to approximate a general problem by a limiting normal problem, a UMP equivalence test is obtained for testing the mean of a multivariate normal mean.