Smooth Simultaneous Confidence Bands For Cumulative Distribution Functions

A plug-in kernel estimator is proposed for H¨older continuous cumulative distribu-tion function (cdf) based on a random sample. In [7], uniform closeness between theproposed estimator and the empirical cdf estimator is established, while the proposedestimator is smooth instead of a step function. A smooth simultaneous confidence bandis constructed based on the smooth distribution estimator and the Kolmogorov distri-bution. Extensive simulation study using two diferent automatic bandwidths confirmsthe theoretical findings.