A Note on Minimax Testing and Confidence Intervals in Moment Inequality Models

Timothy Armstrong

No 1975, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This note uses a simple example to show how moment inequality models used in the empirical economics literature lead to general minimax relative efficiency comparisons. The main point is that such models involve inference on a low dimensional parameter, which leads naturally to a definition of "distance" that, in full generality, would be arbitrary in minimax testing problems. This definition of distance is justified by the fact that it leads to a duality between minimaxity of confidence intervals and tests, which does not hold for other definitions of distance. Thus, the use of moment inequalities for inference in a low dimensional parametric model places additional structure on the testing problem, which leads to stronger conclusions regarding minimax relative efficiency than would otherwise be possible.

Keywords: Minimax; Relative efficiency; Moment inequalities (search for similar items in EconPapers)
JEL-codes: C12 C14 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2014-12
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (3)

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