Abstract
SUMMARY The use of the likelihood function as the minimal sufficient statistic provides a simple and direct proof of results by Barankin and Katz (1959) and Barankin (1961) concerning minimal sufficient statistics. In Section 2 the likelihood function is used to analyse the effect of sampling on the dimensionality of the sufficient statistic and it provides a simple and transparent proof that fixed dimension for the sufficient statistic is restricted to the exponential family. In Section 3 a class of selected exponential distributions is shown to be complete.
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