Chen, Xiaohong, Linton, Oliver and Van Keilegom, Ingrid (2003) Estimation of semiparametric models when the criterion function is not smooth. Econometrics; EM/2003/450, EM/03/450. Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science, London.
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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 like 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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