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Robustness, infinitesimal neighborhoods, and moment restrictions

Author(s): Kitamura, Y; Otsu, T; Evdokimov, Kirill

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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. © 2013 The Econometric Society.
Publication Date: May-2013
Citation: Kitamura, Y, Otsu, T, Evdokimov, K. (2013). Robustness, infinitesimal neighborhoods, and moment restrictions. Econometrica, 81 (3), 1185 - 1201. doi:10.3982/ECTA8617
DOI: doi:10.3982/ECTA8617
ISSN: 0012-9682
EISSN: 1468-0262
Pages: 1185 - 1201
Type of Material: Journal Article
Journal/Proceeding Title: Econometrica
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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