On the multivariatek-sample problem and the generalization of the Kolmogorov-Smirnov-test

Abstract

The objective of this note is to investigate how the classical Kolmogorov-Smirnov two-sample test in p-variate case, as developed by Bickel [2], can be employed in the multivariate k-sample problem. Our approach is based on Statistically Equivalent Blocks (Anderson [1]) which in essence "ranks" vector random variables. The proposed test procedure is distribution-free and consistent against all alternatives.