A class of Stein‐rules in multivariate regression model with structural changes. (5th June 2015)

• Record Type: Journal Article
• Authors: Chen, Fuqi; Nkurunziza, Sévérien
• Is Part Of: Scandinavian journal of statistics. Volume 43:Number 1(2016:Mar.)
• Page Start: 83
• Page End: 102
• Publication Date: 2015-06-05
• Subjects: ADR -- change‐points -- mixingale array -- multivariate regression -- restricted estimator -- shrinkage estimators -- unrestricted estimator; Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12166
• Languages: English
• ISSNs: 0303-6898

Abstract

Abstract: In this paper, we consider an estimation problem of the matrix of the regression coefficients in multivariate regression models with unknown change‐points. More precisely, we consider the case where the target parameter satisfies an uncertain linear restriction. Under general conditions, we propose a class of estimators that includes as special cases shrinkage estimators (SEs) and both the unrestricted and restricted estimator. We also derive a more general condition for the SEs to dominate the unrestricted estimator. To this end, we extend some results underlying the multidimensional version of the mixingale central limit theorem as well as some important identities for deriving the risk function of SEs. Finally, we present some simulation studies that corroborate the theoretical findings.