Year: 1992
Type: article
Abstract: 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.
Source: The Annals of Statistics
Authors: Hanfeng Chen, Wei-Yin Loh
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2088903467