A weighted independence test based on smooth estimation of Kendall distribution

In this study, we introduce a nonparametric test of independence which is based on a weighted Cramer-von Mises distance of the Bernstein estimate of the Kendall distribution function. We examine the power and the size of the new weighted test and, we compare it with the non-weighted nonparametric tests of independence through a Monte Carlo simulation study. The simulation results indicate that both of the choices of the weights and the polynomial degree has a significant effect on the test power. Finally, the procedure is applied to a dataset on chemical elements in water samples for the purpose of illustration.

Automated summary

In this study, a nonparametric test of independence based on a weighted Cramer-von Mises distance of the Bernstein estimate of the Kendall distribution function is introduced. The power and size of the new weighted test are examined and compared with non-weighted nonparametric tests of independence using Monte Carlo simulation. The results indicate that the choice of weights and polynomial degree significantly affects the test power. Finally, the method is applied to a dataset on chemical elements in water samples for illustration.