Hodges-Lehmann Optimality for Testing Moment

Ivan Canay and Taisuke Otsu
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Taisuke Otsu: Cowles Foundation, Yale University, https://cowles.yale.edu/

No 1789, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper studies the Hodges and Lehmann (1956) optimality of tests in a general setup. The tests are compared by the exponential rates of growth to one of the power functions evaluated at a fixed alternative while keeping the asymptotic sizes bounded by some constant. We present two sets of sufficient conditions for a test to be Hodges-Lehmann optimal. These new conditions extend the scope of the Hodges-Lehmann optimality analysis to setups that cannot be covered by other conditions in the literature. The general result is illustrated by our applications of interest: testing for moment conditions and overidentifying restrictions. In particular, we show that (i) the empirical likelihood test does not necessarily satisfy existing conditions for optimality but does satisfy our new conditions; and (ii) the generalized method of moments (GMM) test and the generalized empirical likelihood (GEL) tests are Hodges-Lehmann optimal under mild primitive conditions. These results support the belief that the Hodges-Lehmann optimality is a weak asymptotic requirement.

Keywords: Asymptotic optimality; Large deviations; Moment condition; Generalized method of moments; Generalized empirical likelihood (search for similar items in EconPapers)
JEL-codes: C13 C14 (search for similar items in EconPapers)
Pages: 18 pages
Date: 2011-03
New Economics Papers: this item is included in nep-ecm
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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