BOUNDS ON ARES OF TESTS FOLLOWING BOX-COX-TRANSFORMATIONS
成果类型：
Article
署名作者：
CHEN, HF; LOH, WY
署名单位：
University of Wisconsin System; University of Wisconsin Madison
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176348780
发表日期：
1992
页码：
1485-1500
关键词：
摘要：
Bounds on the asymptotic relative efficiency (ARE) of the Box-Cox transformed two-sample t-test to the ordinary t-test are obtained under local alternatives. It is shown that the ARE is at least 1 for location-shift models. In the case of scale-shift models, a similar bound applies provided the limiting value of the estimated power transformation is greater than 1. If instead the Box-Cox transformed t-test is compared against the ordinary t-test applied to the log-transformed data, then the ARE is bounded below by 1 for all scale-shift models, regardless of the limiting value of the power transformation. The results extend naturally to the multisample F-test. A small simulation study to evaluate the validity of the asymptotic results for finite-sample sizes is also reported.