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Modified sequentially rejective multiple test procedures. (English) Zbl 0603.62087
S. Holm [Scand. J. Stat., Theory Appl. 6, 65-70 (1979; Zbl 0402.62058)] considered a sequentially-rejective method for testing n hypotheses, based on stagewise modification of critical values derived from the simple Bonferroni inequality. The method leads to more powerful tests than the usual nonstagewise Bonferroni method. This paper considers further improvements which result from taking into consideration logical implications among the hypotheses and alternatives. The approach is readily applicable to a wide variety of standard and nonstandard problems.
A number of examples are given and extensions and generalizations are discussed. It is pointed out that the method may be adapted in some circumstances to the use of multiple test procedures based on sharper Bonferroni inequalities or to non-Bonferroni multiple test procedures.

MSC:
62L10 Sequential statistical analysis
62F03 Parametric hypothesis testing
62C25 Compound decision problems in statistical decision theory
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