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.
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Research supported by NSERC Grant No. A3088 and GR-5 Grant from Faculty of Graduate Studies, Carleton University, Ottawa, Canada.
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Kubokawa, T., Robert, C. & Saleh, A.K.M.E. Robust estimation of common regression coefficients under spherical symmetry. Ann Inst Stat Math 43, 677–688 (1991). https://doi.org/10.1007/BF00121647
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DOI: https://doi.org/10.1007/BF00121647