(Received October 20, 1989; revised October 17, 1990)
Abstract. Consider the problem of estimating the common regression coefficients of two linear regression models where the two distributions of the errors may be different and unknown. Under the spherical symmetry assumption, the paper proves the superiority of a Graybill-Deal type combined estimator and the further improvement by the Stein effect which were exhibited by Shinozaki (1978, Comm. Statist. Theory Methods, 7, 1421-1432) in the normal case. This shows the robustness of the dominations since the conditions for the dominations are independent of the errors distributions.
Key words and phrases: Elliptically contoured distribution, heteroscedastic linear model, Stein problem, common mean, Graybill-Deal estimator.
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