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Global and Partial Non-Nested Hypothesesand Asymptotic Local Power

Published online by Cambridge University Press:  11 February 2009

M. Hashem Pesaran
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Abstract

This paper addresses two related issues in theliterature of non-nested hypotheses testing.Firstly, by means of a measure of “closeness” ofprobability density functions, it shows howany two hypotheses can be placedinto the nested and the non-nested categories withthe latter category being subdivided further into“globally” and “partially” non-nested hypotheses.Secondly, by emphasizing the distinction between a“local null” and a “local alternative,” the papershows that only in the case of partially non-nestedhypotheses is it possible to specify localalternatives. In this case the paper derives theasymptotic distribution of the Cox test statisticunder local alternatives and shows that it isdistributed as a normal variate with a mean which isdirectly related to the measure of “closeness” ofthe alternative to the null hypothesis.

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Type
Research Article
Information
Econometric Theory , Volume 3 , Issue 1 , February 1987 , pp. 69 - 97
Copyright
Copyright © Cambridge University Press 1987

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