Bounds and Approximations for Distributions of Weighted Kolmogorov-Smirnov Tests

Nino Kordzakhia () and Alexander Novikov ()
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Nino Kordzakhia: Macquarie University
Alexander Novikov: The University of Technology, Department of Mathematical Sciences

Chapter Chapter 12 in From Statistics to Mathematical Finance, 2017, pp 235-250 from Springer

Abstract: Abstract The paper is motivated by the use of weighted Kolmogorov-Smirnov (wKS) tests in Gene Set Enrichment Analysis where the key requirements are speed and accuracy of computations. We reduce the problem of finding of distributions of one- and two-sided wKS statistics to the nonlinear boundary crossing problem for a Brownian motion. Theoretical estimates of accuracy of the approximations using piecewise linear boundaries are derived. The approximations with 2-knot piecewise linear boundaries are discussed for the one-sided wKS. In the numerical example the estimates of tail probabilities obtained with the use of upper and lower bounds were validated using Monte-Carlo simulation.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-50986-0_12

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DOI: 10.1007/978-3-319-50986-0_12

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