Quantifying the failure of bootstrap likelihood ratio tests
成果类型：
Article
署名作者：
Drton, Mathias; Williams, Benjamin
署名单位：
University of Chicago; University of Chicago
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asr033
发表日期：
2011
页码：
919934
关键词：
摘要：
When testing geometrically irregular parametric hypotheses, the bootstrap is an intuitively appealing method to circumvent difficult distribution theory. It has been shown, however, that the usual bootstrap is inconsistent in estimating the asymptotic distributions involved in such problems. This paper is concerned with the asymptotic size of likelihood ratio tests when critical values are computed using the inconsistent bootstrap. We clarify how the asymptotic size of such a test can be obtained from the size of the corresponding bootstrap test in the relevant limiting normal experiment. For boundary problems, that is, hypotheses given by convex cones, we show the bootstrap test to always be anticonservative, and we compute the size numerically for different two-dimensional examples. The examples illustrate that the size can be below or above the nominal level, and reveal that the relationship between the size of the test and the geometry of the considered hypotheses is surprisingly subtle.
来源URL：