Stepup procedures for control of generalizations of the familywise error rate

By Joseph P. Romano, A. Shaikh. 2006

134 citations recorded by the source corpus.

Consider the multiple testing problem of testing null hypotheses H 1 ,...,H s . A classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of even one false rejection. But if s is large, control of the FWER is so stringent that the ability of a procedure that controls the FWER to detect false null hypotheses is limited. It is therefore desirable to consider other measures of error control. This article considers two generalizations of the FWER. The first is the k-FWER, in which one is willing to tolerate k or more false rejections for some fixed k ≥ I. The second is based on the false discovery proportion (FDP), defined to be the number of false rejections divided by the total number of rejections (and defined to be 0 if there are no rejections). Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289-300] proposed ccntrol of the false discovery rate (FDR), by which they meant that, for fixed a, E(FDP) ≤ a. Here, we consider control of the FDP in the sense that, for fixed y and a, P{FDP > γ} ≤ a. Beginning with any nondecreasing sequence of constants and p-values for the individual tests, we derive stepup procedures that control each of these two measures of error control without imposing any assumptions on the dependence structure of the p-values. We use our results to point out a few interesting connections with some closely related stepdown procedures. We then compare and contrast two FDP-controlling procedures obtained using our results with the stepup procedure for control of the FDR of Benjamini and Yekutieli [Ann. Statist. 29 (2001) 1165-1188].

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/eba852316bbee57005ab2600e4a2fae0a07e1a28

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information (2010, unknown): “single-equilibrium assumption in Bajari, Hong, Krainer, and Nekipelov (2009) and Tang (2009), equilibrium uniqueness in Seim (2006) or Aradillas-Lopez (2009) or parametric specification of equilibrium selection mechanism in some other works).”
Familywise error rate control via knockoffs (2015, methodology): “The step-up procedure is implemented using the critical values suggested in [26], namely their Equation (13).”
Only closed testing procedures are admissible for controlling false discovery proportions (2019, methodology): “A generalization, k-FWER (Finos and Farcomeni, 2011; Guo et al., 2010; Hommel and Hoffmann, 1988; Lehmann and Romano, 2005; Romano and Shaikh, 2006; Sarkar, 2007), makes sure that, for all θ ∈ Θ,”
STEPUP PROCEDURES CONTROLLING GENERALIZED FWER AND GENERALIZED FDR (2007, methodology): “First, we generalize the method of Romano and Shaikh [13] and construct a stepup k-FWER procedure given any set of increasing constants.”
On stepdown control of the false discovery proportion (2006, unknown): “Romano and Shaikh [12] derive stepup procedures which control the k-FWER and the FDP under no dependence assumptions, and some comparisons with stepdown procedures are made as well.”
Control of generalized error rates in multiple testing (2007, methodology): “Some more conservative methods that hold under no dependence assumptions are also developed in [17, 25] and [26].”
Multiple hypothesis testing in experimental economics (2019, methodology): “By arguing as in Theorem 15.4.3 in Lehmann and Romano (2006) and using (d), it follows from the Lindeberg-Feller central limit theorem that An(Pn) d→ N(0, VA(P )) under Pn.”
Control of the false discovery rate under dependence using the bootstrap and subsampling (2008, methodology): “Methods for control of the k-FWER and the FDP based on p-values for each null hypothesis are discussed in Lehmann and Romano (2005a), Romano and Shaikh (2006a), and Romano and Shaikh (2006b).”
Two simple sufficient conditions for FDR control (2008, methodology): “We will prove that the step-down procedure proposed by Benjamini and Liu (1999a) and Romano and Shaikh (2006a) has a controlled FDR under a PRDS-type assumption of H 0 on H 1 ; we also deduce a straightforward generalization to the unspeciﬁed dependencies case.”
Generalizing Simes' test and Hochberg's stepup procedure (2008, methodology): “Then, we get from [13] that the k-FWER of the generalized stepup procedure in the theorem is less than or equal to”
Balanced Control of Generalized Error Rates (2010, background): “(2005a), Romano and Shaikh (2006a), and Romano and Shaikh (2006b) .”