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Econometrics 2018, 6(1), 8; https://doi.org/10.3390/econometrics6010008

Lasso Maximum Likelihood Estimation of Parametric Models with Singular Information Matrices

1,2
and
3,*
1
School of Economics, Shanghai University of Finance and Economics, Shanghai 200433, China
2
Key Laboratory of Mathematical Economics (SUFE), Ministry of Education, Shanghai 200433, China
3
Department of Economics, The Ohio State University, Columbus, OH 43210, USA
*
Author to whom correspondence should be addressed.
Received: 1 December 2017 / Revised: 13 February 2018 / Accepted: 13 February 2018 / Published: 22 February 2018
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Abstract

An information matrix of a parametric model being singular at a certain true value of a parameter vector is irregular. The maximum likelihood estimator in the irregular case usually has a rate of convergence slower than the n -rate in a regular case. We propose to estimate such models by the adaptive lasso maximum likelihood and propose an information criterion to select the involved tuning parameter. We show that the penalized maximum likelihood estimator has the oracle properties. The method can implement model selection and estimation simultaneously and the estimator always has the usual n -rate of convergence. View Full-Text
Keywords: penalized maximum likelihood; singular information matrix; lasso; oracle properties penalized maximum likelihood; singular information matrix; lasso; oracle properties
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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Jin, F.; Lee, L.-F. Lasso Maximum Likelihood Estimation of Parametric Models with Singular Information Matrices. Econometrics 2018, 6, 8.

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