Bootstrapping Oracle Estimators in Sparse Models

• Activity Number: 83
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 4:00 PM to 5:50 PM
• Sponsor: IMS
• Author(s): Mihai Cristian Giurcanu*+ and Brett Presnell
• Companies: University of Louisiana at Lafayette and University of Florida
• Keywords: oracle estimators ; sparse models ; bootstrap ; oracle bootstrap ; LASSO ; inconsistency

Abstract

In this talk, I will first present the large sample behaviour of the standard bootstrap, m-out-of-n bootstrap, and oracle bootstrap (Giurcanu and Presnell, 2009) estimators of the distributions of some oracle estimators which are often used in the estimation of sparse correlation models. These results show that, if the correlation model is sparse, then the standard bootstrap estimators converge in distribution to some random distributions, and thus, they are inconsistent. Furthermore, the m-out-of-n bootstrap and the oracle bootstrap estimators are consistent for all values of the regression coefficients. A local asymptotics analysis describes the behaviour of these oracle estimators as well as of the corresponding bootstrap distribution estimators when some regression parameters are ``small''. In an empirical study, we compare the finite sample properties of the bootstrap estimators for various sample sizes and model parameters.