2016/11/09 by Gavin Lynch, Wenge Guo, Lynch, Gavin +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Decision Sciences · Mathematics · #62J15 #FOS: Computer and information sciences #FOS: Mathematics #Gene expression and cancer classification #Methodology (stat.ME) #Optimal Experimental Design Methods #Statistical Methods in Clinical Trials #Statistics Theory (math.ST) #VLSI and Analog Circuit Testing
paper · pdf · doi:10.48550/arxiv.1611.03146
openalex publication_date 2016/11/09 · openalex created_date 2022/09/20 · openalex updated_date 2026/07/28
Controlling the false discovery rate (FDR) is a powerful approach to multiple\ntesting. In many applications, the tested hypotheses have an inherent\nhierarchical structure. In this paper, we focus on the fixed sequence structure\nwhere the testing order of the hypotheses has been strictly specified in\nadvance. We are motivated to study such a structure, since it is the most basic\nof hierarchical structures, yet it is often seen in real applications such as\nstatistical process control and streaming data analysis. We first consider a\nconventional fixed sequence method that stops testing once an acceptance\noccurs, and develop such a method controlling the FDR under both arbitrary and\nnegative dependencies. The method under arbitrary dependency is shown to be\nunimprovable without losing control of the FDR and unlike existing FDR methods;\nit cannot be improved even by restricting to the usual positive regression\ndependence on subset (PRDS) condition. To account for any potential mistakes in\nthe ordering of the tests, we extend the conventional fixed sequence method to\none that allows more but a given number of acceptances. Simulation studies show\nthat the proposed procedures can be powerful alternatives to existing FDR\ncontrolling procedures. The proposed procedures are illustrated through a real\ndata set from a microarray experiment.\n