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

Tomohiro Ando and Naoya Sueishi
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Tomohiro Ando: Melbourne Business School, University of Melbourne, 200 Leicester Street, Carlton, Victoria 3053, Australia

Econometrics, 2019, vol. 7, issue 1, 1-14

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.

Keywords: diverging number of parameters; penalized empirical likelihood; sparse models (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2019
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