The partitioning principle: a powerful tool in multiple decision theory

By BY H. Finner, K. Strassburger. 2002

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Hochberg's Step-Up Method: Cutting Corners Off Holm's Step-Down Method (2007, methodology): “…version of the Bonferroni test, and Hochberg’s method is thought of as a step-up version of the Bonferroni test, we show in §3 and §4 that both are short cuts of what is now called partition testing, as developed by Stefansson et al. (1988), Hayter & Hsu (1994), and Finner & Strassburger (2002).”
Only closed testing procedures are admissible for controlling false discovery proportions (2019, methodology): “Alternative design principles exist, such as the partitioning principle (Finner and Strassburger, 2002) and sequential rejection (Goeman and Solari, 2010), but these are equivalent to closed testing.”
The Sequential Rejection Principle of Familywise Error Control (2010, methodology): “However, Stefansson, Kim and Hsu (1988) introduced what is now called the partitioning principle, and Finner and Strassburger (2002) showed that the partitioning principle gives a multiple testing procedure that is at least as powerful as closed testing and which may be more powerful in some situati”
Rank verification for exponential families (2016, background): “…of Procedure 1 in the same setting, leading to a lower confidence bound analogous to that of Procedure 2; interestingly, the proof involves a very early application of the partitioning principle, later developed into fundamental technique in multiple comparisons (Finner and Strassburger, 2002).”