Nonparametric estimation of quantile versions of the Bonferroni curve

We consider the quantile versions of the Bonferroni curve and of the Bonferroni index. Distribution-free estimators of these quantile versions are proposed. Asymptotic properties of the estimators are proved. In simulations we compare the accuracy of the estimators. To illustrate the estimators under study, we perform real data analysis concerning the remission times of bladder cancer patients.