Efficiency for Regularization Parameter Selection in Penalized Likelihood Estimation of Misspecified Models

Cheryl J. Flynn, Clifford Hurvich and Jeffrey S. Simonoff

Journal of the American Statistical Association, 2013, vol. 108, issue 503, 1031-1043

Abstract: It has been shown that Akaike information criterion (AIC)-type criteria are asymptotically efficient selectors of the tuning parameter in nonconcave penalized regression methods under the assumption that the population variance is known or that a consistent estimator is available. We relax this assumption to prove that AIC itself is asymptotically efficient and we study its performance in finite samples. In classical regression, it is known that AIC tends to select overly complex models when the dimension of the maximum candidate model is large relative to the sample size. Simulation studies suggest that AIC suffers from the same shortcomings when used in penalized regression. We therefore propose the use of the classical corrected AIC (AIC c ) as an alternative and prove that it maintains the desired asymptotic properties. To broaden our results, we further prove the efficiency of AIC for penalized likelihood methods in the context of generalized linear models with no dispersion parameter. Similar results exist in the literature but only for a restricted set of candidate models. By employing results from the classical literature on maximum-likelihood estimation in misspecified models, we are able to establish this result for a general set of candidate models. We use simulations to assess the performance of AIC and AIC c , as well as that of other selectors, in finite samples for both smoothly clipped absolute deviation (SCAD)-penalized and Lasso regressions and a real data example is considered. Supplementary materials for this article are available online.

Date: 2013
References: View complete reference list from CitEc
Citations: View citations in EconPapers (15)

Downloads: (external link)
http://hdl.handle.net/10.1080/01621459.2013.801775 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:108:y:2013:i:503:p:1031-1043

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UASA20

DOI: 10.1080/01621459.2013.801775

Access Statistics for this article

Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson

More articles in Journal of the American Statistical Association from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().