BOUNDS ON ARES OF TESTS FOLLOWING BOX-COX-TRANSFORMATIONS

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.