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AN AVERAGING ESTIMATOR FOR TWO-STEP M-ESTIMATION IN SEMIPARAMETRIC MODELS

Published online by Cambridge University Press:  07 November 2022

Ruoyao Shi Open the ORCID record for Ruoyao Shi [Opens in a new window]
Ruoyao Shi*
Affiliation:
University of California, Riverside
*
Address correspondence to Ruoyao Shi, Department of Economics, University of California, Riverside, Riverside, CA, USA; e-mail: ruoyao.shi@ucr.edu.
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Abstract

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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, this paper proposes an averaging estimator that combines a semiparametric estimator based on a nonparametric first step and a parametric estimator which imposes parametric restrictions on the first step. The averaging weight is an easy-to-compute sample analog of an infeasible optimal weight that minimizes the asymptotic quadratic risk. Under Stein-type 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 that includes both correct specification and varied degrees of misspecification of the parametric restrictions, and the asymptotic upper bound is weakly less than zero. The averaging estimator, along with an easy-to-implement inference method, is demonstrated in an example.

Type
ARTICLES
Information
Econometric Theory , Volume 40 , Issue 3 , June 2024 , pp. 652 - 687
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

The comments from the Editor (Peter C.B. Phillips), the Associate Editor (Patrik Guggenberger), and two anonymous referees were vastly helpful in improving this paper. The author also thanks Colin Cameron, Xu Cheng, Denis Chetverikov, Yanqin Fan, Jinyong Hahn, Bo Honoré, Toru Kitagawa, Zhipeng Liao, Hyungsik Roger Moon, Whitney Newey, Geert Ridder, Aman Ullah, Haiqing Xu, and the participants at various seminars and conferences for helpful comments. This project was generously supported by UC Riverside Regents’ Faculty Fellowship 2019–2020. Zhuozhen Zhao provided great research assistance. All remaining errors are the author’s.

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