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Bounds and Approximations for Distributions of Weighted Kolmogorov-Smirnov Tests

In: From Statistics to Mathematical Finance

Author

Listed:
  • Nino Kordzakhia

    (Macquarie University)

  • Alexander Novikov

    (The University of Technology, Department of Mathematical Sciences)

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.

Suggested Citation

  • Nino Kordzakhia & Alexander Novikov, 2017. "Bounds and Approximations for Distributions of Weighted Kolmogorov-Smirnov Tests," Springer Books, in: Dietmar Ferger & Wenceslao González Manteiga & Thorsten Schmidt & Jane-Ling Wang (ed.), From Statistics to Mathematical Finance, chapter 0, pages 235-250, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-50986-0_12
    DOI: 10.1007/978-3-319-50986-0_12
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