A class of locally optimal tests based on linear functions of certain transformations of independent test statistics is proposed and studied. These overall tests are useful in combining independent tests for certain multivariate or multiparameter hypotheses where local optimality is interpreted in a specialized sense. For the two-sample case, along with the expressions for the null distributions of the test statistics, tabulations of percentile points are provided.
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Monti et al. (1976) studied this question.
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