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Estimation of Semiparametric Models When the Criterion Function Is Not Smooth
Xiaohong Chen, Oliver Linton and Ingrid Van Keilegom
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
You can always find the topics here!Topics: Estimators, Statistical estimation, Mathematical independent variables, Economic models, Estimation methods, Linear regression, Semiparametric modeling, Economic theory, Statistical models, Consistent estimators
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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.
Econometrica © 2003 The Econometric Society