Econometrica: May 2013, Volume 81, Issue 3

Robustness, Infinitesimal Neighborhoods, and Moment Restrictions
p. 1185-1201

Yuichi Kitamura, Taisuke Otsu, Kirill Evdokimov

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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Supplement "Robustness, Infinitesimal Neighborhoods, and Moment Restrictions"

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Supplement to "Robustness, Infinitesimal Neighborhoods, and Moment Restrictions"

This appendix presents the proofs of some of the results presented in the previous sections.

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