Abstract
This paper is concerned with the problems of making statistical inferences on stochastic processes. It will be restricted to the case, of white Gaussian processes. The object of this paper is to determine a hypothesis testing procedure for a simple hypothesis versus a composite alternative. Investigations are carried out here for the case where the domain of the stochastic parameter is the unit circle. Composite alternatives are handled by considering only those tests which remain invariant under the group of rotations for the unit circle. The paper will consist of two parts. Part I will be of concern when only one sample function of the process is tested. In this case besides the uniformly most powerful invariant test, the Bayes solution and the test based on the least favorable distribution are also found. In Part II the sequential counterpart of Part I is considered. Here the best invariant test is found.
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