Locally Optimal Testing When a Nuisance Parameter Is Present Only under the Alternative

Maxwell King and Thomas S Shively

The Review of Economics and Statistics, 1993, vol. 75, issue 1, 1-7

Abstract: The authors consider hypothesis testing problems in which a nuisance parameter is present only under the alternative hypothesis. Standard asymptotic tests, such as likelihood ratio, Lagrange multiplier and Wald tests, are difficult to apply because o f problems incurred in obtaining their asymptotic distributions. To overcome this difficulty, the authors reparameterize the testing problem to one for which an exact small sample test can be construct ed using existing hypothesis testing procedures. The reparameterization technique is applied to two examples from the econometrics literatur e, and an empirical power comparison shows that their test has better power properties than tests previously proposed in the literature. Further, p-values for their test can be computed. in O(n) operations so the test can be implemented efficiently. Copyright 1993 by MIT Press.

Date: 1993
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