Abstract

<jats:p>If the probability differential of a set of stochastic variates contains <jats:italic>k</jats:italic> unknown parameters, the statistical hypotheses concerning them may be simple or composite. The hypothesis leading to a complete specification of the values of the <jats:italic>k</jats:italic> 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.</jats:p>