Bounds and approximations for distributions of weighted Kolmogorov-Smirnov tests

Kordzakhia, N; Novikov, A

Bounds and approximations for distributions of weighted Kolmogorov-Smirnov tests

Kordzakhia, N Novikov, A

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Publication Type:: Chapter
Citation:: From Statistics to Mathematical Finance: Festschrift in Honour of Winfried Stute, 2017, pp. 235 - 250
Issue Date:: 2017-01-01

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Field	Value	Language
dc.contributor.author	Kordzakhia, N	en_US
dc.contributor.author	Novikov, A https://orcid.org/0000-0001-8529-173X	en_US
dc.date.issued	2017-01-01	en_US
dc.identifier.citation	From Statistics to Mathematical Finance: Festschrift in Honour of Winfried Stute, 2017, pp. 235 - 250	en_US
dc.identifier.isbn	9783319509853	en_US
dc.identifier.uri	http://hdl.handle.net/10453/126270
dc.description.abstract	© Springer International Publishing AG 2017. 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.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DP150102758
dc.relation.ispartof	From Statistics to Mathematical Finance: Festschrift in Honour of Winfried Stute	en_US
dc.relation.isbasedon	10.1007/978-3-319-50986-0_12	en_US
dc.title	Bounds and approximations for distributions of weighted Kolmogorov-Smirnov tests	en_US
dc.type	Chapter
utslib.for	0101 Pure Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	closed_access
pubs.publication-status	Published	en_US

Abstract:

© Springer International Publishing AG 2017. 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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http://hdl.handle.net/10453/126270