A Generalization on Combining Estimation Problems Under Quadratic Loss

• Activity Number: 261
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Sévérien Nkurunziza*
• Companies: University of Windsor/Université de Sherbrooke
• Keywords: Elliptically contoured variate ; Least-squares estimators ; Quadratic loss ; Semiparametric inference ; Shrinkage estimators ; Stein-type estimator

Abstract

In this paper, we generalize the main result in Judge and Mittelhammer [Judge, G. G., and Mittelhammer, R. (2004), A Semiparametric Basis for Combining Estimation Problems under Quadratic Loss; JASA, 99, 466, 479-487] which stipulates that, in the context of nonzero correlation, a sufficient condition for the Stein rule (SR)-type estimator to dominate the base estimator is that the dimension k should be at least 5. In particular, we present a class of estimators which includes the SR estimator as a special case. Further, we prove that, for any member of this class, k > 3 is a sufficient condition regardless of the correlation factor. We also relax the Gaussian condition of the distribution of the base estimator, as we consider the family of elliptically contoured variates. The simulation studies corroborate our theoretical findings for small and moderate sample sizes. The proposed method is applied to the Cigarette dataset produced by the USA Federal Trade Commission.