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Estimation of Semiparametric Models When the Criterion Function Is Not Smooth

Xiaohong Chen, Oliver Linton and Ingrid Van Keilegom
Econometrica
Vol. 71, No. 5 (Sep., 2003), pp. 1591-1608
Published by: The Econometric Society
Stable URL: http://www.jstor.org/stable/1555514
Page Count: 18
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Estimation of Semiparametric Models When the Criterion Function Is Not Smooth
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Abstract

We provide easy to verify sufficient conditions for the consistency and asymptotic normality of a class of semiparametric optimization estimators where the criterion function does not obey standard smoothness conditions and simultaneously depends on some nonparametric estimators that can themselves depend on the parameters to be estimated. Our results extend existing theories such as those of Pakes and Pollard (1989), Andrews (1994a), and Newey (1994). We also show that bootstrap provides asymptotically correct confidence regions for the finite dimensional parameters. We apply our results to two examples: a 'hit rate' and a partially linear median regression with some endogenous regressors.

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