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Abstract and Applied Analysis
Volume 2014, Article ID 391719, 16 pages
Research Article

Moment Conditions Selection Based on Adaptive Penalized Empirical Likelihood

1China University of Petroleum, Qingdao 266580, China
2Shandong University Qilu Securities Institute for Financial Studies, Shandong University, Jinan 250100, China

Received 30 March 2014; Revised 29 May 2014; Accepted 5 June 2014; Published 13 July 2014

Academic Editor: Caihong Li

Copyright © 2014 Yunquan Song. 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.


Empirical likelihood is a very popular method and has been widely used in the fields of artificial intelligence (AI) and data mining as tablets and mobile application and social media dominate the technology landscape. This paper proposes an empirical likelihood shrinkage method to efficiently estimate unknown parameters and select correct moment conditions simultaneously, when the model is defined by moment restrictions in which some are possibly misspecified. We show that our method enjoys oracle-like properties; that is, it consistently selects the correct moment conditions and at the same time its estimator is as efficient as the empirical likelihood estimator obtained by all correct moment conditions. Moreover, unlike the GMM, our proposed method allows us to carry out confidence regions for the parameters included in the model without estimating the covariances of the estimators. For empirical implementation, we provide some data-driven procedures for selecting the tuning parameter of the penalty function. The simulation results show that the method works remarkably well in terms of correct moment selection and the finite sample properties of the estimators. Also, a real-life example is carried out to illustrate the new methodology.