On the Convergence Rate of the SCAD-Penalized Empirical Likelihood Estimator
This paper investigates the asymptotic properties of a penalized empirical likelihood estimator for moment restriction models when the number of parameters (<inline-formula> <math display="inline"> <semantics> <msub> <mi>p</mi> <mi>n</mi> <...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-03-01
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| Series: | Econometrics |
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| Online Access: | https://www.mdpi.com/2225-1146/7/1/15 |
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| author | Tomohiro Ando Naoya Sueishi |
| author_facet | Tomohiro Ando Naoya Sueishi |
| author_sort | Tomohiro Ando |
| collection | DOAJ |
| description | This paper investigates the asymptotic properties of a penalized empirical likelihood estimator for moment restriction models when the number of parameters (<inline-formula> <math display="inline"> <semantics> <msub> <mi>p</mi> <mi>n</mi> </msub> </semantics> </math> </inline-formula>) and/or the number of moment restrictions increases with the sample size. Our main result is that the SCAD-penalized empirical likelihood estimator is <inline-formula> <math display="inline"> <semantics> <msqrt> <mrow> <mi>n</mi> <mo>/</mo> <msub> <mi>p</mi> <mi>n</mi> </msub> </mrow> </msqrt> </semantics> </math> </inline-formula>-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 <inline-formula> <math display="inline"> <semantics> <msqrt> <mrow> <mi>n</mi> <mo>/</mo> <msub> <mi>p</mi> <mi>n</mi> </msub> </mrow> </msqrt> </semantics> </math> </inline-formula>-consistency and an oracle property are satisfied simultaneously. As far as we know, this paper is the first to specify sufficient conditions for both <inline-formula> <math display="inline"> <semantics> <msqrt> <mrow> <mi>n</mi> <mo>/</mo> <msub> <mi>p</mi> <mi>n</mi> </msub> </mrow> </msqrt> </semantics> </math> </inline-formula>-consistency and the oracle property of the penalized empirical likelihood estimator. |
| first_indexed | 2024-04-11T13:59:20Z |
| format | Article |
| id | doaj.art-5fb49071fe4f4451865db7c1f3425d65 |
| institution | Directory Open Access Journal |
| issn | 2225-1146 |
| language | English |
| last_indexed | 2024-04-11T13:59:20Z |
| publishDate | 2019-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Econometrics |
| spelling | doaj.art-5fb49071fe4f4451865db7c1f3425d652022-12-22T04:20:11ZengMDPI AGEconometrics2225-11462019-03-01711510.3390/econometrics7010015econometrics7010015On the Convergence Rate of the SCAD-Penalized Empirical Likelihood EstimatorTomohiro Ando0Naoya Sueishi1Melbourne Business School, University of Melbourne, 200 Leicester Street, Carlton, Victoria 3053, AustraliaGraduate School of Economics, Kobe University, 2-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, JapanThis paper investigates the asymptotic properties of a penalized empirical likelihood estimator for moment restriction models when the number of parameters (<inline-formula> <math display="inline"> <semantics> <msub> <mi>p</mi> <mi>n</mi> </msub> </semantics> </math> </inline-formula>) and/or the number of moment restrictions increases with the sample size. Our main result is that the SCAD-penalized empirical likelihood estimator is <inline-formula> <math display="inline"> <semantics> <msqrt> <mrow> <mi>n</mi> <mo>/</mo> <msub> <mi>p</mi> <mi>n</mi> </msub> </mrow> </msqrt> </semantics> </math> </inline-formula>-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 <inline-formula> <math display="inline"> <semantics> <msqrt> <mrow> <mi>n</mi> <mo>/</mo> <msub> <mi>p</mi> <mi>n</mi> </msub> </mrow> </msqrt> </semantics> </math> </inline-formula>-consistency and an oracle property are satisfied simultaneously. As far as we know, this paper is the first to specify sufficient conditions for both <inline-formula> <math display="inline"> <semantics> <msqrt> <mrow> <mi>n</mi> <mo>/</mo> <msub> <mi>p</mi> <mi>n</mi> </msub> </mrow> </msqrt> </semantics> </math> </inline-formula>-consistency and the oracle property of the penalized empirical likelihood estimator.https://www.mdpi.com/2225-1146/7/1/15diverging number of parameterspenalized empirical likelihoodsparse models |
| spellingShingle | Tomohiro Ando Naoya Sueishi On the Convergence Rate of the SCAD-Penalized Empirical Likelihood Estimator Econometrics diverging number of parameters penalized empirical likelihood sparse models |
| title | On the Convergence Rate of the SCAD-Penalized Empirical Likelihood Estimator |
| title_full | On the Convergence Rate of the SCAD-Penalized Empirical Likelihood Estimator |
| title_fullStr | On the Convergence Rate of the SCAD-Penalized Empirical Likelihood Estimator |
| title_full_unstemmed | On the Convergence Rate of the SCAD-Penalized Empirical Likelihood Estimator |
| title_short | On the Convergence Rate of the SCAD-Penalized Empirical Likelihood Estimator |
| title_sort | on the convergence rate of the scad penalized empirical likelihood estimator |
| topic | diverging number of parameters penalized empirical likelihood sparse models |
| url | https://www.mdpi.com/2225-1146/7/1/15 |
| work_keys_str_mv | AT tomohiroando ontheconvergencerateofthescadpenalizedempiricallikelihoodestimator AT naoyasueishi ontheconvergencerateofthescadpenalizedempiricallikelihoodestimator |