2014/06/23 by Jay Bartroff, Bartroff, Jay · 1 citation
Decision Sciences · Mathematics · #62J15 #62L10 #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1406.5933
openalex publication_date 2014/06/23 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
The \γ-FDP and k-FWER multiple testing error metrics, which are tail\nprobabilities of the respective error statistics, have become popular recently\nas less-stringent alternatives to the FDR and FWER. We propose general and\nflexible stepup and stepdown procedures for testing multiple hypotheses about\nsequential (or streaming) data that simultaneously control both the type I and\nII versions of \γ-FDP, or k-FWER. The error control holds regardless of\nthe dependence between data streams, which may be of arbitrary size and shape.\nAll that is needed is a test statistic for each data stream that controls the\nconventional type I and II error probabilities, and no information or\nassumptions are required about the joint distribution of the statistics or data\nstreams. The procedures can be used with sequential, group sequential,\ntruncated, or other sampling schemes. We give recommendations for the\nprocedures' implementation including closed-form expressions for the needed\ncritical values in some commonly-encountered testing situations. The proposed\nsequential procedures are compared with each other and with comparable fixed\nsample size procedures in the context of strongly positively correlated\nGaussian data streams. For this setting we conclude that both the stepup and\nstepdown sequential procedures provide substantial savings over the fixed\nsample procedures in terms of expected sample size, and the stepup procedure\nperforms slightly but consistently better than the stepdown for \γ-FDP\ncontrol, with the relationship reversed for k-FWER control.\n