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September, 1992 Bounds on AREs of Tests Following Box-Cox Transformations
Hanfeng Chen, Wei-Yin Loh
Ann. Statist. 20(3): 1485-1500 (September, 1992). DOI: 10.1214/aos/1176348780


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.


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Hanfeng Chen. Wei-Yin Loh. "Bounds on AREs of Tests Following Box-Cox Transformations." Ann. Statist. 20 (3) 1485 - 1500, September, 1992.


Published: September, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0781.62055
MathSciNet: MR1186261
Digital Object Identifier: 10.1214/aos/1176348780

Primary: 62G20
Secondary: 62G10

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.20 • No. 3 • September, 1992
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