Robustness, infinitesimal neighborhoods, and moment restrictions

Yuichi Kitamura, Taisuke Otsu, Kirill Evdokimov

Research output: Contribution to journalArticle

14 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1185-1201
Number of pages17
JournalEconometrica
Volume81
Issue number3
DOIs
Publication statusPublished - 2013 May 1
Externally publishedYes

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Keywords

  • Asymptotic Minimax Theorem
  • Hellinger distance
  • Semiparametric efficiency

ASJC Scopus subject areas

  • Economics and Econometrics

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