ADMISSIBLE, SIMILAR TESTS: A CHARACTERIZATION
Montiel Olea, JosÃ© Luis
Econometric Theory, 2020, vol. 36, issue 2, 347-366
This article studies a classical problem in statistical decision theory: a hypothesis test of a sharp null in the presence of a nuisance parameter. The main contribution of this article is a characterization of two finite-sample properties often deemed reasonable in this environment: admissibility and similarity. Admissibility means that a test cannot be improved uniformly over the parameter space. Similarity requires the null rejection probability to be unaffected by the nuisance parameter.The characterization result has two parts. The first partâ€”established by Chernozhukov, Hansen, and Jansson (2009, Econometric Theory 25, 806â€“818)â€”states that maximizing weighted average power (WAP) subject to a similarity constraint suffices to generate admissible, similar tests. The second partâ€”hereby establishedâ€”states that constrained WAP maximization is (essentially) a necessary condition for a test to be admissible and similar. The characterization result shows that choosing an admissible, similar test is tantamount to selecting a particular weight function to report weighted average power. This result applies to full vector inference with a nuisance parameter, not to subvector inference.The article also revisits the theory of testing in the instrumental variables model. Specificallyâ€”and in light of the relevance of the weighted average power criterion in the main theoretical resultâ€”the article suggests a weight function for the structural parameters of the homoskedastic instrumental variables model, based on the priors proposed by Chamberlain (2007). The corresponding test is, by construction, admissible and similar. In addition, the test is shown to have finite- and large-sample properties comparable to those of the conditional likelihood ratio test.
References: Add references at CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
https://www.cambridge.org/core/product/identifier/ ... type/journal_article link to article abstract page (text/html)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:cup:etheor:v:36:y:2020:i:2:p:347-366_6
Access Statistics for this article
More articles in Econometric Theory from Cambridge University Press Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK.
Bibliographic data for series maintained by Keith Waters ().