A multivariate Kolmogorov- Smirnov test of goodness of fit

Abstract _ This paper presents a distribution free multivariate Kolmogorov-Smirnov good- ness of fit test. The test uses an statistic which is built using Rosenblatt's transformation and an algorithm is developed to compute it in the bivariate case. An approximate test, that can be easily computed in any dimension, is also presented. The power of these multivariate tests is studied in a simulation study. Key words: Empirical distribution function. Kolmogorov-Smirnov statistics. Rosenblatt's transformation