Robustness, Infinitesimal Neighborhoods, and Moment Restrictions

Authors

  • Yuichi Kitamura,

    1. Cowles Foundation for Research in Economics, Yale University, New Haven, CT 06520, U.S.A.; yuichi.kitamura@yale.edu
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  • Taisuke Otsu,

    1. Dept. of Economics, London School of Economics and Political Science, Houghton Street, London, WC2A 2AE, U.K.; t.otsu@lse.ac.uk
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  • Kirill Evdokimov

    1. Dept. of Economics, Princeton University, Princeton, NJ 08544, U.S.A.; kevdokim@princeton.edu
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    • We are grateful to a co-editor and two anonymous referees for helpful remarks and suggestions. We thank participants at the CIREQ Conference on GMM, the 2007 Winter Meetings of the Econometric Society, the 2007 Netherlands Econometrics Study Group Annual Conference, and seminars at Boston University, Chicago Booth, Harvard-MIT, LSE, NYU, Ohio State, Seoul National University, Texas A&M, the University of Tokyo, Vanderbilt, and Wisconsin for valuable comments. We acknowledge financial support from the National Science Foundation via Grants SES-0241770, SES-0551271, and SES-0851759 (Kitamura) and SES-0720961 (Otsu).


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 is 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.

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