Titlebook: Selected Works of Debabrata Basu; Anirban DasGupta Book 2011 Springer Science+Business Media, LLC 2011 D. Basu.Debabrata Basu.selected wor

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Selected Works of Debabrata Basu978-1-4419-5825-9Series ISSN 2197-5825 Series E-ISSN 2197-5833

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On Statistics Independent of a Complete Sufficient Statistic,dent random variables such that their joint distribution involves an unknown location parameter . then there can exist a linear boundedly complete sufficient statistic for . only if the .’s are all normal. Similar characterizations for the Gamma distribution also are indicated.

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Basu on Ancillarity,arded as simply an application of the sufficiency principle (SP), since as a function of the data the whole likelihood function (. a positive constant factor — a gloss we shall henceforth take as read) is minimal sufficient; but that principle says nothing about what we should do with the likelihood function when we have it.

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The Family of Ancillary Statistics, of their information content is attempted here. In general there are many maximal ancillaries, Among the minimal ancillaries there exists a unique largest one. When there exists a complete sufficient statistic, the problem of tracking down the maximal and minimal ancillaries becomes greatly simplified.

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Basu on Ancillarity,ihood function as embodying all the information that the data had to supply about the unknown parameter. At a purely abstract level, this might be regarded as simply an application of the sufficiency principle (SP), since as a function of the data the whole likelihood function (. a positive constant

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