Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation

C. Radhakrishna Raoa1

a1 King's College Cambridge

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.

(Received April 18 1947)