Abstract
This paper investigates the asymptotic properties of a penalized empirical likelihood estimator for moment restriction models when the number of parameters (p) 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/Pn-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 both √n/Pn-consistency and an oracle property are satisfied simultaneously. Our results provide a solid theoretical support to the penalized empirical likelihood estimator of Leng and Tang (2012).
Highlights
Sparse regression models have received considerable attention in business, economics, genetics, and various other fields
Estimator for moment restriction models, when the number of parameters and/or the number of moment restrictions increases with the sample size
This paper shows that the penalized empirical likelihood (PEL) estimator satisfies the oracle property in the sense of
Summary
Sparse regression models have received considerable attention in business, economics, genetics, and various other fields. There is a large literature on instrument (moment) selection that addresses the problem of selecting/constructing optimal instruments when a large number of instruments are available (e.g., Donald and Newey 2001; Bai and Ng 2009; Kuersteiner and Okui 2010; Belloni et al 2012; Caner and Fan 2015; Cheng and Liao 2015; Shi 2016a). In contrast to these papers, here we focus on variable selection in a structural model.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
