If the probability differential of a set of stochastic variates contains k unknown parameters, the statistical hypotheses concerning them may be simple or composite. The hypothesis leading to a complete specification of the values of the k parameters is called a simple hypothesis, and the one leading to a collection of admissible sets a composite hypothesis. In this paper we shall be concerned with the testing of these two types of hypotheses on the basis of a large number of observations from any probability distribution satisfying some mild restrictions and their use in problems of estimation.
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C. Radhakrishna Rao (1948) studied this question.