Shrinkage Estimation and Lasso in Linear Model with Unknown Change-Points

• Activity Number: 698
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: SSC
• Author(s): Fuqi Chen*+ and Sévérien Nkurunziza
• Companies: University of Windsor and The University of Windsor
• Keywords: Stein-rule ; Unrestricted estimator ; Restricted estimator ; change-point ; Lasso ; shrinkage estimator

Abstract

In this presentation, we will discuss an estimation problem in linear model with unknown change-points, when an uncertain prior information is available. More precisely, the regression coefficients are suspected to be restricted to a linear subspace while the "change-points" are treated as unknown parameters to be estimated as well. Also, we relax some assumptions, which are commonly given in literature, about the linear model with change-points, and we derive the asymptotic properties of the the unrestricted and the restricted estimators. Further, we propose a class of improved estimators which includes as special cases the unrestricted and the restricted estimators as well as James-Stein type estimators. We prove that the derived shrinkage estimators dominate in mean square error sense the unrestricted estimator. The proposed methodology works for both matrix and vector parameters cases. In order to illustrate the performance of the proposed method, we perform some simulation studies which corroborate our theoretical findings.