Approximations for weighted Kolmogorov–Smirnov distributions via boundary crossing probabilities

Kordzakhia, N; Novikov, A; Ycart, B

Approximations for weighted Kolmogorov–Smirnov distributions via boundary crossing probabilities

Kordzakhia, N Novikov, A

Ycart, B

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Publication Type:: Journal Article
Citation:: Statistics and Computing, 2017, 27 (6), pp. 1513 - 1523
Issue Date:: 2017-11-01

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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.contributor.author	Ycart, B	en_US
dc.date.issued	2017-11-01	en_US
dc.identifier.citation	Statistics and Computing, 2017, 27 (6), pp. 1513 - 1523	en_US
dc.identifier.issn	0960-3174	en_US
dc.identifier.uri	http://hdl.handle.net/10453/114752
dc.description.abstract	© 2016, The Author(s). A statistical application to Gene Set Enrichment Analysis implies calculating the distribution of the maximum of a certain Gaussian process, which is a modification of the standard Brownian bridge. Using the transformation into a boundary crossing problem for the Brownian motion and a piecewise linear boundary, it is proved that the desired distribution can be approximated by an n-dimensional Gaussian integral. Fast approximations are defined and validated by Monte Carlo simulation. The performance of the method for the genomics application is discussed.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DP150102758
dc.relation.ispartof	Statistics and Computing	en_US
dc.relation.isbasedon	10.1007/s11222-016-9701-y	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.title	Approximations for weighted Kolmogorov–Smirnov distributions via boundary crossing probabilities	en_US
dc.type	Journal Article
utslib.citation.volume	6	en_US
utslib.citation.volume	27	en_US
utslib.for	0802 Computation Theory and Mathematics	en_US
utslib.for	0104 Statistics	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	open_access
pubs.issue	6	en_US
pubs.publication-status	Published	en_US
pubs.volume	27	en_US

Abstract:

© 2016, The Author(s). A statistical application to Gene Set Enrichment Analysis implies calculating the distribution of the maximum of a certain Gaussian process, which is a modification of the standard Brownian bridge. Using the transformation into a boundary crossing problem for the Brownian motion and a piecewise linear boundary, it is proved that the desired distribution can be approximated by an n-dimensional Gaussian integral. Fast approximations are defined and validated by Monte Carlo simulation. The performance of the method for the genomics application is discussed.

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http://hdl.handle.net/10453/114752