The Large-Sample, Small Disturbance and Asymptotic Conditions of Dominance of Efficient Shrinkage in Seemingly Unrelated Regression Equations (SURE)

• Activity Number: 357 - Contributed Poster Presentations: Business and Economic Statistics Section
• Type: Contributed
• Date/Time: Tuesday, July 30, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Ali Mehrabani*
• Keywords: Shrinkage; James-Stein; SUR models; Restricted Estimator; Unrestricted Estimator

Abstract

We propose an efficient shrinkage estimator in SURE. The shrinkage estimator shrinks Zellner’s (1962) generalized least square (GLS) estimator toward a user-specified restricted GLS estimator. Following Hansen (2016), the shrinkage weight is inversely proportional to the Wald-test statistic which evaluates the null of parameter homogeneity against the alternative hypothesis of parameter heterogeneity. The approximate bias, second moment matrix, and approximate distribution of the shrinkage estimator using large-sample and small-disturbance expansions are provided. We also derive the asymptotic bias and mean square error (MSE) of the shrinkage estimator using a general local asymptotic framework and give the conditions under which the shrinkage estimator dominates the unrestricted estimator on the basis of their MSEs. Also, the conditions for dominance of the shrinkage estimator over the unrestricted estimator are made on the basis of their MSEs, and their concentrations of probability computed by means of asymptotic expansions of their distributions when the disturbance variance tends to zero and alternatively when the sample size increases indefinitely.