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ROBUSTNESS, INFINITESIMAL NEIGHBORHOODS, AND MOMENT RESTRICTIONS

By Yuichi Kitamura, Taisuke Otsu and Kirill Evdokimov

Abstract

Abstract. This paper explores robust estimation of parameters identified by a set of moment restrictions. Suppose the econometrician observes data generated from a perturbed version of the probability distribution that corresponds to the true parameter value. Such perturbation can be regarded as a consequence of data errors, misspecification and other factors, following the literature of robust statistical estimation. There are two aspects in assessing robustness properties of an estimator. One is about bias, that is, the effect of the perturbation of the data generating mechanism on the behavior of the limit of the estimator. The other is about dispersion, often measured by the asymptotic variance. As far as one considers global perturbation, the former factor typically dominates, thereby making the latter a second order issue. An alternative approach is to consider the effect of local perturbation within shrinking topological neighborhoods of the original probability distribution, so that both bias and variance matter asymptotically. Such analysis, put loosely, enables the researcher to assess robustness in terms of asymptotic mean squared error (MSE). This paper derives asymptotic optimality results in moment restriction models along this line of analysis. To be added

Topics: Empirical Likelihood, Hellinger Distance, Robust Estimation
Year: 2014
OAI identifier: oai:CiteSeerX.psu:10.1.1.415.1623
Provided by: CiteSeerX
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