Efficiently combining data from various sources

Abstract

In this paper, we revisit the main result in Judge and Mittelhammer [Judge, G. G., and Mittelhammer, R. (2004) [6], 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-type estimators to dominate the base estimator is that the dimension k should be at least 5. We prove that $$k\geqslant 3$$ is a sufficient condition regardless of the correlation factor. This theoretical finding is corroborated by some simulation studies. The proposed method is applied to the Cigarette dataset produced by the USA Federal Trade Commission.