Nonparametric kk-sample test based on kernel density estimator for paired design

Comparing whether the marginal distribution functions of a kk-dimensional random variable are equal or not is a classical problem in statistical inference. Usually, the parametric ANOVA repeat measures analysis or the nonparametric Friedman test are used. Both procedures allow us to detect differences among the location parameters but not among shapes or spreads of the involved distributions. The ACAC statistic which is based on the measure of the common area under the respective kernel density estimators is used in order to compare the equality among the marginal densities of a kk-dimensional random variable. The BM algorithm is employed to select, automatically, the final bandwidth parameter. Its statistical power is studied from Monte Carlo simulations and a real data analysis is also considered.