Characterization of the asymptotic distribution of semiparametric M-estimators

Hidehiko Ichimura, Sokbae Lee

Research output: Contribution to journalArticle

25 Scopus citations

Abstract

This paper develops a concrete formula for the asymptotic distribution of two-step, possibly non-smooth semiparametric M-estimators under general misspecification. Our regularity conditions are relatively straightforward to verify and also weaker than those available in the literature. The first-stage nonparametric estimation may depend on finite dimensional parameters. We characterize: (1) conditions under which the first-stage estimation of nonparametric components do not affect the asymptotic distribution, (2) conditions under which the asymptotic distribution is affected by the derivatives of the first-stage nonparametric estimator with respect to the finite-dimensional parameters, and (3) conditions under which one can allow non-smooth objective functions. Our framework is illustrated by applying it to three examples: (1) profiled estimation of a single index quantile regression model, (2) semiparametric least squares estimation under model misspecification, and (3) a smoothed matching estimator.

Original languageEnglish (US)
Pages (from-to)252-266
Number of pages15
JournalJournal of Econometrics
Volume159
Issue number2
DOIs
StatePublished - Dec 2010
Externally publishedYes

Keywords

  • Semiparametric estimation
  • Two-step estimators

ASJC Scopus subject areas

  • Economics and Econometrics

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