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Finner, H.; Strassburger, K.

The partitioning principle: a powerful tool in multiple decision theory. (English) Zbl 1029.62064

Ann. Stat. 30, No. 4, 1194-1213 (2002).
Summary: A first general principle and nowadays state of the art for the construction of powerful multiple test procedures controlling a multiple level \(\alpha\) is the so-called closure principle. We introduce another powerful tool for the construction of multiple decision procedures, especially for the construction of multiple test procedures and selection procedures. This tool is based on a partition of the parameter space and will be called partitioning principle (PP).
In the first part of the paper we review basic concepts of multiple hypotheses testing and discuss a slight generalization of the current theory. In the second part we present various variants of the PP for the construction of multiple test procedures, these are a general PP (GPP), a weak PP (WPP) and a strong PP (SPP). It will be shown that, depending on the underlying decision problem, a PP may lead to more powerful test procedures than a formal application of the closure principle (FCP). Moreover, the more complex SPP may be more powerful than the WPP. Based on a duality between testing and selecting, PPs can also be applied for the construction of more powerful selection procedures. In the third part of the paper FCP, WPP and SPP are applied and compared in some examples.

Cited in 1 Review
Cited in 37 Documents

MSC:

62J15 Paired and multiple comparisons; multiple testing
62C99 Statistical decision theory
62F03 Parametric hypothesis testing
62F07 Statistical ranking and selection procedures

Keywords:

directional errors; formal closure principle; multiple comparisons; multiple levels; strong and weak multiple partitioning principles
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References:

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