Bounds and approximations for distributions of weighted Kolmogorov-Smirnov tests

Nino Kordzakhia; Alexander Novikov

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

Bounds and approximations for distributions of weighted Kolmogorov-Smirnov tests

Nino Kordzakhia^*, Alexander Novikov

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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.

Original language	English
Title of host publication	From Statistics to Mathematical Finance
Subtitle of host publication	Festschrift in Honour of Winfried Stute
Editors	Dietmar Ferger, Thorsten Schmidt, Wenceslao González Manteiga, Jane-Ling Wang
Place of Publication	Switzerland
Publisher	Springer, Springer Nature
Pages	235-250
Number of pages	16
ISBN (Electronic)	9783319509860
ISBN (Print)	9783319509853
DOIs	https://doi.org/10.1007/978-3-319-50986-0_12
Publication status	Published - 2017

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

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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.",

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Bounds and approximations for distributions of weighted Kolmogorov-Smirnov tests. / Kordzakhia, Nino; Novikov, Alexander.
From Statistics to Mathematical Finance: Festschrift in Honour of Winfried Stute. ed. / Dietmar Ferger; Thorsten Schmidt; Wenceslao González Manteiga; Jane-Ling Wang. Switzerland: Springer, Springer Nature, 2017. p. 235-250.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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AU - Novikov, Alexander

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AB - 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.

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Bounds and approximations for distributions of weighted Kolmogorov-Smirnov tests

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