Robustness, Infinitesimal Neighborhoods, and Moment Restrictions

Yuichi Kitamura (), Taisuke Otsu () and Kirill Evdokimov
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Yuichi Kitamura: Cowles Foundation, Yale University, http://cowles.econ.yale.edu/faculty/kitamura.htm
Taisuke Otsu: Cowles Foundation, Yale University, http://cowles.econ.yale.edu/faculty/otsu.htm
Kirill Evdokimov: Dept. of Economics, Yale University, http://www.econ.yale.edu/

No 1720, Cowles Foundation Discussion Papers from Cowles Foundation, Yale University

Abstract: This paper is concerned with robust estimation under moment restrictions. A moment restriction model is semiparametric and distribution-free, therefore it imposes mild assumptions. Yet it is reasonable to expect that the probability law of observations may have some deviations from the ideal distribution being modeled, due to various factors such as measurement errors. It is then sensible to seek an estimation procedure that are robust against slight perturbation in the probability measure that generates observations. This paper considers local deviations within shrinking topological neighborhoods to develop its large sample theory, so that both bias and variance matter asymptotically. The main result shows that there exists a computationally convenient estimator that achieves optimal minimax robust properties. It is semiparametrically efficient when the model assumption holds, and at the same time it enjoys desirable robust properties when it does not.

Keywords: Asymptotic minimax theorem; Hellinger distance; Semiparametric efficiency (search for similar items in EconPapers)
JEL-codes: C10 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2009-08
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