© 1977 by Biometrika Trust
Hypothesis testing when a nuisance parameter is present only under the alternative
Applied Mathematics Division, Department of Scientific and Industrial Research Wellington, New Zealand
Suppose that the distribution of a random variable representing the outcome of an experiment depends on two parameters 
and 
and that we wish to test the hypothesis = 0 against the alternative > 0. If the distribution does not depend on when = 0, standard asymptotic methods such as likelihood ratio testing or C(
) testing are not directly applicable. However, these methods may, under appropriate conditions, be used to reduce the problem to one involving inference from a Gaussian process. This simplified problem is examined and a test which may be derived as a likelihood ratio test or from the union-intersection principle is introduced. Approximate expressions for the significance level and power are obtained.
Key Words: (C-alpha test • Hypothesis testing • Likelihood ratio test • Maximum of Gaussian process • Simple hypothesis • Union-intersection principle
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