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October, 1995 Tests Following Transformations
Hanfeng Chen
Ann. Statist. 23(5): 1587-1593 (October, 1995). DOI: 10.1214/aos/1176324314


Chen and Loh showed that the Box-Cox transformed two-sample $t$-test is more powerful than the ordinary $t$-test under Pitman alternatives where the location shifts appear in the untransformed scale. In this article, we prove that Chen and Loh's result also holds for a general family of transformations. An upper bound on the asymptotic relative efficiency (ARE) is obtained. In addition, we investigate bounds on the ARE under Pitman location shift alternatives in the transformed scale. We find that when the estimate for $\lambda$ is consistent, a lower bound on the ARE is the reciprocal of Fisher information of the standard transformed distribution. This lower bound is close to 1 for commonly used symmetric distributions.


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Hanfeng Chen. "Tests Following Transformations." Ann. Statist. 23 (5) 1587 - 1593, October, 1995.


Published: October, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0843.62024
MathSciNet: MR1370298
Digital Object Identifier: 10.1214/aos/1176324314

Primary: 62F05
Secondary: 62E20 , 62F03 , 62F35 , 62G20

Keywords: Asymptotic relative efficiency , Box-Cox power transformation , Fisher information , Pitman alternative , two-sample problem

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 5 • October, 1995
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