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Estimation of Semiparametric Models when the Criterion Function Is Not Smooth
Author(s) -
Chen Xiaohong,
Linton Oliver,
Van Keilegom Ingrid
Publication year - 2003
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/1468-0262.00461
Subject(s) - estimator , mathematics , asymptotic distribution , smoothness , consistency (knowledge bases) , nonparametric statistics , semiparametric regression , semiparametric model , function (biology) , econometrics , statistics , mathematical analysis , evolutionary biology , biology , geometry
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.