Summary
The problem of estimating the multidimensional location parameter is considered. The new family of multivariate distribution is characterized by the property of the independence of the best equivariant estimator on the even loss function choice. Some generalizations of known functional equations are introduced and solved for this aim.
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References
J. Aczel. (1966). Lectures on Functional Equations and Their Applications, Academic Press.
A. M. Kagan, Yu. V. Linnik, C. R. Rao (1973). Characterization Problems in Mathematical Statistics. John Wiley and Sons, N. Y.
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A. L. Rukhin (1970). Soviet Math. Dokl. II, 1, 89–92
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© 1975 D. Reidel Publishing Company, Dordrecht-Holland
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Rukhin, A.L. (1975). The Families with a “Universal” Location Estimator. In: Patil, G.P., Kotz, S., Ord, J.K. (eds) A Modern Course on Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1842-5_13
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DOI: https://doi.org/10.1007/978-94-010-1842-5_13
Publisher Name: Springer, Dordrecht
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