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 journalArticle

    4 Citations (Scopus)
    2 Downloads (Pure)

    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 languageEnglish
    Pages (from-to)1513-1523
    Number of pages11
    JournalStatistics and Computing
    Volume27
    Issue number6
    DOIs
    Publication statusPublished - 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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