COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1720 Robustness, Infinitesimal Neighborhoods, and Moment Restrictions Yuichi Kitamura, Taisuke Otsu and Kirill Evdokimov August 2009 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 are
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. |
