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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Váldodahkkit: Tomohiro Ando, Naoya Sueishi
Materiálatiipa: Artihkal
Giella:English
Almmustuhtton: MDPI AG 2019-03-01
Ráidu:Econometrics
Fáttát:
Liŋkkat:https://www.mdpi.com/2225-1146/7/1/15
Govvádus
Čoahkkáigeassu: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.
ISSN:2225-1146