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.
@article{1176348780,
author = {Chen, Hanfeng and Loh, Wei-Yin},
title = {Bounds on AREs of Tests Following Box-Cox Transformations},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 1485-1500},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348780}
}
Chen, Hanfeng; Loh, Wei-Yin. Bounds on AREs of Tests Following Box-Cox Transformations. Ann. Statist., Tome 20 (1992) no. 1, pp. 1485-1500. http://gdmltest.u-ga.fr/item/1176348780/