This book establishes the theoretical foundations of a general methodology for multiple hypothesis testing and discusses its software implementation in R and SAS. The methods are applied to a range of testing problems in biomedical and genomic research, including the identification of differentially expressed and co-expressed genes in high-throughput gene expression experiments, such as microarray experiments; tests of association between gene expression measures and biological annotation metadata (e.g., Gene Ontology); sequence analysis; and the genetic mapping of complex traits using single nucleotide polymorphisms. The book is aimed at both statisticians interested in multiple testing theory and applied scientists encountering high-dimensional testing problems in their subject matter area. Specifically, the book proposes resampling-based single-step and stepwise multiple testing procedures for controlling a broad class of Type I error rates, defined as tail probabilities and expected values for arbitrary functions of the numbers of Type I errors and rejected hypotheses (e.g., false discovery rate). Unlike existing approaches, the procedures are based on a test statistics joint null distribution and provide Type I error control in testing problems involving general data generating distributions (with arbitrary dependence structures among variables), null hypotheses, and test statistics. The multiple testing results are reported in terms of rejection regions, parameter confidence regions, and adjusted p-values.

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