  Gene Set Enrichment Analysis (GSEA) is a basic tool for genomic data
treatment. From a statistical point of view, the centering of its test
statistic does not allow the derivation of asymptotic results. A test statistic
with a different centering is proposed. Under the null hypothesis, the
convergence in distribution of the new test statistic is proved, using the
theory of empirical processes. The limiting distribution can be computed by
Monte-Carlo simulation. The test defined in this way has been called Weighted
Kolmogorov Smirnov (WKS) test. The fact that the evaluation of the asymptotic
distribution serves for many different gene sets results in shorter computing
times. Using expression data from the GEO repository, tested against the MSig
Database C2, a comparison between the classical GSEA test and the new procedure
has been conducted. Our conclusion is that, beyond its mathematical and
algorithmic advantages, the WKS test could be more informative in many cases,
than the classical GSEA test.
