On the usage of randomized p-values in the Schweder–Spjøtvoll estimator View Full Text


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Article Info

DATE

2021-04-28

AUTHORS

Anh-Tuan Hoang, Thorsten Dickhaus

ABSTRACT

We consider multiple test problems with composite null hypotheses and the estimation of the proportion π0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _{0}$$\end{document} of true null hypotheses. The Schweder–Spjøtvoll estimator π^0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hat{\pi }}_0$$\end{document} utilizes marginal p-values and relies on the assumption that p-values corresponding to true nulls are uniformly distributed on [0, 1]. In the case of composite null hypotheses, marginal p-values are usually computed under least favorable parameter configurations (LFCs). Thus, they are stochastically larger than uniform under non-LFCs in the null hypotheses. When using these LFC-based p-values, π^0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hat{\pi }}_0$$\end{document} tends to overestimate π0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _{0}$$\end{document}. We introduce a new way of randomizing p-values that depends on a tuning parameter c∈[0,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c \in [0,1]$$\end{document}. For a certain value c=c⋆\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c = c^{\star }$$\end{document}, the resulting bias of π^0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hat{\pi }}_0$$\end{document} is minimized. This often also entails a smaller mean squared error of the estimator as compared to the usage of LFC-based p-values. We analyze these points theoretically, and we demonstrate them numerically in simulations. More... »

PAGES

1-31

References to SciGraph publications

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URI

http://scigraph.springernature.com/pub.10.1007/s10463-021-00797-0

DOI

http://dx.doi.org/10.1007/s10463-021-00797-0

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https://app.dimensions.ai/details/publication/pub.1137566709


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