Scan Statistic Tail Probability Assessment Based on Process Covariance and Window Size
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A scan statistic is examined for the purpose of testing the existence of a global peak in a random process with dependent variables of any distribution. The scan statistic tail probability is obtained based on the covariance of the moving sums process, thereby accounting for the spatial nature of the data as well as the size of the searching window. Exact formulas linking this covariance to the window size and the correlation coefficient are developed under general, common and auto covariance structures of the variables in the original process. The implementation and applicability of the formulas are demonstrated on multiple processes of t-statistics, treating also the case of unknown covariance. A sensitivity analysis provides further insight into the variant interaction of the tail probability with the influence parameters. An R code for the tail probability computation and the data analysis is offered within the supplementary material.
KeywordsScan statistic Tail probability Moving sums Covariance structure Peak detection Sequence search
Mathematics Subject Classification (2010)62G32 62J15 30C40
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- Bates D, Maechler M (2010) Matrix: sparse and dense matrix classes and methods. R package version 0.999375-46. Retrieved from http://CRAN.R-project.org/package=Matrix
- Chen J (1998) Approximations and inequalities for discrete scan statistics. unpublished Ph.D. Dissertation, University of Connecticut, Storrs, CTGoogle Scholar
- Genz A (1992) Numerical computation of multivariate normal probabilities. J Comput Graph Stat 1:141–150Google Scholar
- Genz A (1993) Comparison of methods for the computation of multivariate normal probabilities. Computing Science and Statistics 25:400–405Google Scholar
- Genz A, Bretz F, Miwa T, Mi X, Leisch F, Scheipl F, Hothorn T (2014) mvtnorm: multivariate normal and t distributions. R package version 0.9-9996. http://CRAN.R-project.org/package=mvtnorm
- Hoh J, Ott J (2000) Scan statistics to scan markers for susceptibility genes. Proc Natl Acad Sci:120–130Google Scholar
- R Development Core Team (2011) R: A language and environment for statistical computing. Foundation for statistical computing, ISBN 3-900051-07-0. Vienna, Austria. Retrieved from http://www.R-project.org/
- Schäfer J, Strimmer K (2005) A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Statistical Applications in Genetics and Molecular Biology, 4, Article 32Google Scholar
- Schäfer J, Opgen-Rhein R, Zuber V, Ahdesmaki M, Pedro Duarte Silva A, Strimmer K (2013) corpcor: efficient estimation of covariance and (Partial) correlation. R package version 1.6.6. http://strimmerlab.org/software/corpcor/