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Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models
Author(s) -
Chen Xiaohong,
Pouzo Demian
Publication year - 2015
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta10771
Subject(s) - mathematics , wald test , estimator , nonparametric statistics , quasi likelihood , asymptotic distribution , sieve (category theory) , statistics , statistical hypothesis testing , negative binomial distribution , combinatorics , poisson distribution
This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals, which include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. These models are often ill‐posed and hence it is difficult to verify whether a (possibly nonlinear) functional is root‐ n estimable or not. We provide computationally simple, unified inference procedures that are asymptotically valid regardless of whether a functional is root‐ n estimable or not. We establish the following new useful results: (1) the asymptotic normality of a plug‐in penalized sieve minimum distance (PSMD) estimator of a (possibly nonlinear) functional; (2) the consistency of simple sieve variance estimators for the plug‐in PSMD estimator, and hence the asymptotic chi‐square distribution of the sieve Wald statistic; (3) the asymptotic chi‐square distribution of an optimally weighted sieve quasi likelihood ratio (QLR) test under the null hypothesis; (4) the asymptotic tight distribution of a non‐optimally weighted sieve QLR statistic under the null; (5) the consistency of generalized residual bootstrap sieve Wald and QLR tests; (6) local power properties of sieve Wald and QLR tests and of their bootstrap versions; (7) asymptotic properties of sieve Wald and SQLR for functionals of increasing dimension. Simulation studies and an empirical illustration of a nonparametric quantile IV regression are presented.