An Averaging Estimator for Two Step M Estimation in Semiparametric Models

Ruoyao Shi ()

No 202105, Working Papers from University of California at Riverside, Department of Economics

Abstract: In a two step extremum estimation (M estimation) framework with a finite dimensional parameter of interest and a potentially infinite dimensional first step nuisance parameter, I propose an averaging estimator that combines a semiparametric estimator based on nonparametric first step and a parametric estimator which imposes parametric restrictions on the first step. The averaging weight is the sample analog of an infeasible optimal weight that minimizes the asymptotic quadratic risk. I show that under mild conditions, the asymptotic lower bound of the truncated quadratic risk difference between the averaging estimator and the semiparametric estimator is strictly less than zero for a class of data generating processes (DGPs) that includes both correct specification and varied degrees of misspecification of the parametric restrictions, and the asymptotic upper bound is weakly less than zero.

Keywords: two step M estimation; semiparametric model; averaging estimator; uniform dominance; asymptotic quadratic risk (search for similar items in EconPapers)
JEL-codes: C13 C14 C51 C52 (search for similar items in EconPapers)
Pages: 47 Pages
Date: 2021-02
New Economics Papers: this item is included in nep-ecm
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