×

Multiple testing of two-sided alternatives with dependent data. (English) Zbl 1149.62009

Summary: Multiple testing procedures have become an integral element of analysis in many practical problems. The development of sound procedures has become an important statistical issue. Many procedures have been suggested and many criteria of goodness have been used. Most recent procedures are stepwise in nature. Perhaps the most fundamental (and typically overlooked) issue is the behavior of the multiple testing procedure as it relates to each individual testing problem.
We study two of the most popular stepwise procedures. We demonstrate that the individual tests they induce are inadmissible in some important two-sided testing models when correlation is present. That is, for each individual hypothesis testing problem, a test exists whose size is less than or equal to that of the stepwise procedure test and whose power is greater than or equal to the stepwise procedure test with some strict inequality. This means that the overall multiple testing procedure is inadmissible whenever a loss based on the number of Type I and Type II errors is used.

MSC:

62F03 Parametric hypothesis testing
62C15 Admissibility in statistical decision theory
62J15 Paired and multiple comparisons; multiple testing
62J05 Linear regression; mixed models
PDFBibTeX XMLCite
Full Text: Link