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It is proved that if there exists a sufficient statistic for the estimation of an unknown parameter of a population, the frequency function of the population must be of a certain type. It is shown that some modification of previous theory of the intrinsic accuracy of statistics is necessary when the range of the population sampled is a function of the parameter to be estimated. Finally, the theory is extended to sufficient sets of statistics, i.e. sets of statistics which together contain all the information provided by a sample about an unknown parameter.
E. J. G. Pitman (Tue,) studied this question.