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[In this chapter, we will discuss multiple hypothesis-testing issues from a frequentist perspective. The Bayesian approaches for multiple-testing problems will be discussed briefly in Chap. 10. As we all know, a typical hypothesis test in the frequentist paradigm can be written as 1.1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${H}_{o} : \delta \in {\Omega }_{0}\ \mathrm{or}\ {H}_{a} : \delta \in {\Omega }_{1},$$ \end{document} where δ is a parameter such as treatment effect, the domain Ω0 can be, for example, a set of nonpositive values, and the domain Ω1 can be the negation of Ω0. In this case, (1.1) becomes 1.2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${H}_{o} : \delta \leq 0\ \mathrm{or}\ {H}_{a} : \delta > 0.$$ \end{document}]
Published: Jun 16, 2011
Keywords: False Discovery Rate; Closure Principle; True Null Hypothesis; Stepup Procedure; Simultaneous Confidence Interval
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