Abstract
In an earlier paper (1955) the author stated that any statistic independent of a sufficient statistic must have the same distribution for all values of the unknown parameter. An example is given here to show that the proposition is not true in the generality stated above. Conditions under which the proposition is true are discussed.
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Basu, D. (1955): On statistics independent of a complete sufficient statistic. Sankhyā, 15, 377.
Fisher, R. A. (1921): The mathematical foundations of theoretical statistics. Phil. Trans. Royal Soc. A, 222, 309.
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Basu, D. (2011). On Statistics Independent of Sufficient Statistics. In: DasGupta, A. (eds) Selected Works of Debabrata Basu. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5825-9_16
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DOI: https://doi.org/10.1007/978-1-4419-5825-9_16
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