Concentration and goodness-of-fit in higher dimensions: (Asymptotically) distribution-free methods
成果类型：
Article
署名作者：
Polonik, W
署名单位：
University of California System; University of California Davis
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
1999
页码：
1210-1229
关键词：
摘要：
A novel approach for constructing goodness-of-fit techniques in arbitrary (finite) dimensions is presented. Testing problems are considered as well as the construction of diagnostic plots. The approach is based on some new notions of mass concentration, and in fact, our basic testing problems are formulated as problems of goodness-of-concentration. It is this connection to concentration of measure that makes the approach conceptually simple. The presented test statistics are continuous functionals of certain processes which behave Like the standard one-dimensional uniform empirical process. Hence, the test statistics behave like classical test statistics for goodness-of-fit. In particular, for simple hypotheses they are asymptotically distribution free with well-known asymptotic distribution. The simple technical idea behind the approach may be called a generalized quantile transformation, where the role of one-dimensional quantiles in classical situations is taken over by so-called minimum volume sets.