On optimality of stepdown and stepup multiple test procedures

By Erich Leo Lehmann, Joseph P. Romano, J. Shaffer. 2005

55 citations recorded by the source corpus.

Consider the multiple testing problem of testing k null hypotheses, where the unknown family of distributions is assumed to satisfy a certain monotonicity assumption. Attention is restricted to procedures that control the familywise error rate in the strong sense and which satisfy a monotonicity condition. Under these assumptions, we prove certain maximin optimality results for some well-known stepdown and stepup procedures.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f270419418f21a09a2c47a3ab464a3bc4f0651fa

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Control of generalized error rates in multiple testing (2007, background): “In some problems, [19] show that such stepwise procedures are optimal in a certain sense, in the case k = 1.”
Overview of Friedman’s Test and Post-hoc Analysis (2015, background): “Hochberg e Hommel are step-up procedures where testing begins with the hypothesis associated with the least significant test statistic and continues in increasing order of significance as long no rejection occurs or there are no more hypotheses to test (Lehmann et al., 2005; Tamhane et al., 1998).”
To How Many Simultaneous Hypothesis Tests Can Normal, Student's t or Bootstrap Calibration Be Applied? (2006, background): “…(2003), Donoho and Jin (2004), Efron (2004), Genovese and Wasserman (2004), Storey, Taylor, and Siegmund (2004), Lehmann and Romano (2005), and Lehmann, Romano, and Shaffer (2005), where many new ideas have been introduced to control different aspects of simultaneous hypothesis testing and…”
Optimal weighting for false discovery rate control (2008, background): “In Roquain and van de Wiel (2008), we proposed some extensions of the present FDR control results to the case of positively regressively dependence or unspecified dependence.”
The optimal discovery procedure: a new approach to simultaneous significance testing (2007, unknown): “See Shaffer (1995) for a review of optimality in terms of the familywise error rate, as well as the more recent Lehmann et al. (2005).”
Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing (2005, background): “In some problems where a monotonicity condition holds (distinct from the monotonicity assumption here), Lehmann, Romano, and Shaffer (2003) showed that such stepwise procedures are optimal in a maximin sense.”
The Bayes oracle and asymptotic optimality of multiple testing procedures under sparsity (2010, methodology): “s of step-up multiple testing procedures controlling FDR. In recent years many new multiple testing procedures, which have some optimality properties in the classical sense, have been proposed (e.g., [11, 29, 32] or [33]). In [20] an asymptotic analysis is performed and new step-up and step-up-down ”