Abstract
A plug-in kernel estimator is proposed for Hölder continuous cumulative distribution function (cdf) based on a random sample. Uniform closeness between the proposed estimator and the empirical cdf estimator is established, while the proposed estimator is smooth instead of a step function. A smooth simultaneous confidence band is constructed based on the smooth distribution estimator and the Kolmogorov distribution. Extensive simulation study using two different automatic bandwidths confirms the theoretical findings.
Acknowledgements
This research has been supported in part by NSF Award DMS 1007594, Jiangsu Specially-Appointed Professor Program and Jiangsu Key Discipline Program (Statistics), Jiangsu, China. The helpful comments by the Editor-in-Chief and two referees are gratefully acknowledged.