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Econometrics 2019, 7(1), 15; https://doi.org/10.3390/econometrics7010015

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

1
Melbourne Business School, University of Melbourne, 200 Leicester Street, Carlton, Victoria 3053, Australia
2
Graduate School of Economics, Kobe University, 2-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan
*
Author to whom correspondence should be addressed.
Received: 18 October 2018 / Revised: 18 March 2019 / Accepted: 18 March 2019 / Published: 20 March 2019
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PDF [283 KB, uploaded 20 March 2019]

Abstract

This paper investigates the asymptotic properties of a penalized empirical likelihood estimator for moment restriction models when the number of parameters ( p n ) 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 / p n -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 n / p n -consistency and an oracle property are satisfied simultaneously. As far as we know, this paper is the first to specify sufficient conditions for both n / p n -consistency and the oracle property of the penalized empirical likelihood estimator. View Full-Text
Keywords: diverging number of parameters; penalized empirical likelihood; sparse models diverging number of parameters; penalized empirical likelihood; sparse models
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Ando, T.; Sueishi, N. On the Convergence Rate of the SCAD-Penalized Empirical Likelihood Estimator. Econometrics 2019, 7, 15.

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