On the Convergence Rate of the SCAD-Penalized Empirical Likelihood Estimator

16 Pages Posted: 7 Dec 2017

See all articles by Tomohiro Ando

Tomohiro Ando

University of Melbourne - Melbourne Business School

Naoya Sueishi

Kobe University - Graduate School of Economics

Date Written: November 29, 2017

Abstract

This paper investigates the asymptotic properties of a penalized empirical likelihood estimator for moment restriction models when the number of parameters (p) and/or the number of moment restrictions increases with the sample size. Our main result is that the SCAD-penalized empirical likelihood estimator is √n/Pn-consistent under a reasonable condition on the regularization parameter. Our consistency rate is better than the existing ones. This paper also provides sufficient conditions under which both √n/Pn-consistency and an oracle property are satisfied simultaneously. Our results provide a solid theoretical support to the penalized empirical likelihood estimator of Leng and Tang (2012).

Keywords: Diverging number of parameters, Penalized empirical likelihood, Sparse models

JEL Classification: C14, C52

Suggested Citation

Ando, Tomohiro and Sueishi, Naoya, On the Convergence Rate of the SCAD-Penalized Empirical Likelihood Estimator (November 29, 2017). Available at SSRN: https://ssrn.com/abstract=3079386 or http://dx.doi.org/10.2139/ssrn.3079386

Tomohiro Ando

University of Melbourne - Melbourne Business School ( email )

200 Leicester Street
Carlton, Victoria 3053 3186
Australia

Naoya Sueishi (Contact Author)

Kobe University - Graduate School of Economics ( email )

2-1, Rokkodai
Nada-Ku
Kobe, Hyogo, 657-8501
Japan

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