Abstract
This paper contains a theorem connected with Y. V. Linnik’s conjecture on conditions of independence of a pair of normal sample statistics, which are continuous and homogeneous. These properties are significant for the problem, as it is seen from the proof.
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References
A. A. Zinger and Y. V. Linnik, “Polynomial Statistics of a Normal Sample”, Dokl. Akad. Nauk SSSR 176 (4), 766–767 (1967).
Y. V. Linnik, Lećons sur les problèmes de statistique analytique (Gauthiers-Villars, Bokforlaget Natur och Kultur, Paris–Stockholm, 1968).
A. M. Kagan, Y. V. Linnik, and C. R. Rao, Characterization Problems in Mathematical Statistics (Wiley, New York, 1973).
E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge Univ. Press, Cambridge, 1927), Part. 2.
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Zinger, A.A. On unlinking of continuous statistics of normal sample. Math. Meth. Stat. 26, 154–158 (2017). https://doi.org/10.3103/S1066530717020053
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DOI: https://doi.org/10.3103/S1066530717020053