Approximations for weighted Kolmogorov–Smirnov distributions via boundary crossing probabilities

Nino Kordzakhia; Alexander Novikov; Bernard Ycart

doi:10.1007/s11222-016-9701-y

Approximations for weighted Kolmogorov–Smirnov distributions via boundary crossing probabilities

Nino Kordzakhia, Alexander Novikov, Bernard Ycart^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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Abstract

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.

Original language	English
Pages (from-to)	1513-1523
Number of pages	11
Journal	Statistics and Computing
Volume	27
Issue number	6
DOIs	https://doi.org/10.1007/s11222-016-9701-y
Publication status	Published - Nov 2017

Bibliographical note

Copyright the Author(s) 2016. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Keywords

Boundary crossing
Gene set enrichment analysis
P value approximation

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10.1007/s11222-016-9701-y

Publisher version (open access)Final published version, 340 KBLicence: CC BY

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AU - Novikov, Alexander

AU - Ycart, Bernard

N1 - Copyright the Author(s) 2016. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

PY - 2017/11

Y1 - 2017/11

N2 - 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.

AB - 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.

KW - Boundary crossing

KW - Gene set enrichment analysis

KW - P value approximation

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UR - http://purl.org/au-research/grants/arc/DP150102758

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JO - Statistics and Computing

JF - Statistics and Computing

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ER -

Approximations for weighted Kolmogorov–Smirnov distributions via boundary crossing probabilities

Abstract

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Keywords

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