2008/10/28 by Wenge Guo, Guo, Wenge, M. Bhaskara Rao +1 · 1 citation
Decision Sciences · Mathematics · #62J15 (Primary) 62G10 (Secondary) #FOS: Mathematics #Optimal Experimental Design Methods #Statistical Methods and Bayesian Inference #Statistical Methods in Clinical Trials #Statistics Theory (math.ST) #math.ST #msc:62G10 #msc:62J15 #stat.TH
paper · pdf · doi:10.48550/arxiv.0810.5004
Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)
arxiv created 2008/10/28 · openalex publication_date 2008/10/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A classical approach for dealing with the multiple testing problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of at least one false rejection. In many applications, one might be willing to tolerate more than one false rejection provided the number of such cases is controlled, thereby increasing the ability of the procedure to detect false null hypotheses. This suggests replacing control of the FWER by controlling the probability of k or more false rejections, which is called the k-FWER. In this article, a unified approach is presented for deriving the k-FWER controlling procedures. We first generalize the well-known closure principle in the context of the FWER to the case of controlling the k-FWER. Then, we discuss how to derive the k-FWER controlling stepwise (stepdown or stepup) procedures based on marginal p-values using this principle. We show that, under certain conditions, generalized closed testing procedures can be reduced to stepwise procedures, and any stepwise procedure is equivalent to a generalized closed testing procedure. Finally, we generalize the well-known Hommel procedure in two directions, and show that any generalized Hommel procedure is equivalent to a generalized closed testing procedure with the same critical values.