On the Efficiency of a Semiparametric Approach to the One-Way Layout
A semiparametric approach to the one-way layout is described, and its efficiency in the two-sample case relative to the common t-test is studied. The power efficiency computed for several special cases points to an intriguing behavior where one test can be more efficient than the other over a certain parameter range and less efficient over some other range. Given m random samples from m distributions, the method holds one distribution as “reference” and treats the other distributions as “distortions” of the reference. The combined sample is used in the semiparametric estimation of the reference distribution and its distortions, and in testing the hypothesis of distribution equality. An application to microarray data illustrates the main ideas, and also motivates the question of power efficiency.
AMS Subject ClassificationPrimary 62F05 Secondary 62F10 92B05
KeywordsProfile likelihood hypothesis test exponential distortion Pitman efficiency gene expression cDNA
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