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Classes of Similar Regions and Their PowerProperties for Some Econometric TestingProblems

Published online by Cambridge University Press:  11 February 2009

Grant H. Hillier
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Abstract

In an hypothesis testing problem involving nuisanceparameters for which boundedly complete sufficientstatistics exist under the null hypothesis, theclass of all similar regions for the problem ischaracterized by the conditional distribution of thedata given these sufficient statistics. If thereexists a one-to-one transformationy → (t, u) ofthe data, y, to the sufficientstatistic, t, and a second vectorof statistics, u, that isindependent of t under the nullhypothesis, then the statistic uitself characterizes the class of similar regions.This paper applies this idea to five testingproblems of interest in econometrics. In each casewe obtain the density of the relevant statisticunder the null hypothesis, when it is free ofnuisance parameters, and under the alternative.Using the density under the alternative, we discussthe power properties of the class of similar testsfor each problem. Other applications are alsosuggested.

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Type
Research Article
Information
Econometric Theory , Volume 3 , Issue 1 , February 1987 , pp. 1 - 44
Copyright
Copyright © Cambridge University Press 1987

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