Confidence-Region Tests

Summary To test a hypothesis that a parameter has value θ* we usually ask whether an observation falls in a critical region of the outcome space. It is well known that, by a suitable choice of confidence region, an equivalent test is to ask whether θ* lies outside the confidence region. In this paper the concept of such a confidence-region test is extended in directions which are relevant to the study of data-snooping and multiple-hypothesis testing. These problems are investigated for linear models and, in the asymptotic case, for more general parametric models.