Approximations for weighted Kolmogorov–Smirnov distributions via boundary crossing probabilities

Publication Type:
Journal Article
Statistics and Computing, 2017, 27 (6), pp. 1513 - 1523
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© 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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