Approximations for weighted Kolmogorov–Smirnov distributions via boundary crossing probabilities

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.
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http://hal.univ-grenoble-alpes.fr/hal-01879590
Contributeur : Brigitte Bidégaray-Fesquet <>
Soumis le : lundi 24 septembre 2018 - 10:16:35
Dernière modification le : jeudi 11 juillet 2019 - 11:42:05

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Nino Kordzakhia, Alexander Novikov, Bernard Ycart. Approximations for weighted Kolmogorov–Smirnov distributions via boundary crossing probabilities. Statistics and Computing, Springer Verlag (Germany), 2017, 27 (6), pp.1513-1523. ⟨10.1007/s11222-016-9701-y⟩. ⟨hal-01879590⟩

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