Characterization of the asymptotic distribution of semiparametric M-estimators

Hidehiko Ichimura (1) , Sokbae Lee (2)

1 UTokyo - The University of Tokyo
2 Department of Economics

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.

Mots clés: C13; C14; Semiparametric estimation; Two-step estimators

Domaines: Econométrie de la finance [q-fin.ST]

Hidehiko Ichimura, Sokbae Lee. Characterization of the asymptotic distribution of semiparametric M-estimators. Econometrics, 2010, 159 (2), pp.252. ⟨10.1016/j.jeconom.2010.05.005⟩. ⟨hal-00741628⟩