Nonparametric Two-Step Sieve M Estimation and Inference

Posted: 23 Mar 2016

See all articles by Jinyong Hahn

Jinyong Hahn

University of California, Los Angeles

Zhipeng Liao

University of California, Los Angeles (UCLA) - Department of Economics

Geert Ridder

University of Southern California

Date Written: March 1, 2016

Abstract

This paper studies the two-step sieve M estimation of general semi/nonparametric models, where the second step involves sieve estimation of unknown functions that may use the nonparametric estimates from the first step as inputs, and the parameters of interest are functionals of unknown functions estimated in both steps. We establish the asymptotic normality of the plug-in two-step sieve M estimate of a functional that could be root-n estimable. They asymptotic variance may not have a closed form expression, but can be approximated by a sieve variance that characterizes the effect of the first-step estimation on the second-step estimates. We provide a simple consistent estimate of the sieve variance and hence a Wald type inference based on the Gaussian approximation. The finite sample performance of the two-step estimator and the proposed inference procedure are investigated in a simulation study.

Keywords: Two-Step Sieve Estimation; Nonparametric Generated Regressors; Asymptotic Normality; Sieve Variance Estimation

JEL Classification: C14, C31, C32

Suggested Citation

Hahn, Jinyong and Liao, Zhipeng and Ridder, Geert, Nonparametric Two-Step Sieve M Estimation and Inference (March 1, 2016). USC-INET Research Paper No. 16-07, Available at SSRN: https://ssrn.com/abstract=2750193 or http://dx.doi.org/10.2139/ssrn.2750193

Jinyong Hahn (Contact Author)

University of California, Los Angeles ( email )

405 Hilgard Avenue
Box 951361
Los Angeles, CA 90095-1361
United States

Zhipeng Liao

University of California, Los Angeles (UCLA) - Department of Economics ( email )

8283 Bunche Hall
Los Angeles, CA 90095-1477
United States

Geert Ridder

University of Southern California ( email )

Kaprielian Hall
Los Angeles, CA 90089
United States
213-740-2110 (Phone)
213-740-8543 (Fax)

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