A generalized family of multiple test procedures

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Abstract
A new family of multiple test procedures is devised. The members of the family are linked through a parameter that gives flexibility in adapting the procedure to the alternative hypothesis. Some known procedures, such as Fisher's and Tippet's combination procedures are members of the proposed family. A few properties of the new family are examined. In particular, it is shown that for an appropriate value of the link parameter, the procedures are consonant, in the sense of Gabriel (1969), and strongly control the family-wise error rate (Hochberg & Tamhane, 1987). In addition, the procedures can be made robust in terms of type-one error control when the test statistics are not independent.