Abstract
Two new properties of the kernel distribution function estimator of diverse nature are derived. Firstly, a law of the iterated logarithm is proved for both the integrated absolute error and the integrated squared error of the estimator. Secondly, the maximal smoothing principle in kernel density estimation developed by Terrell is extended to kernel distribution function estimation, which allows, among others, the derivation of an alternative quick-and-simple bandwidth selector. In fact, there is a common link between the two topics: both problems are solved through the use of the same, not-so-standard, methodology. The results based on simulated data and a real data set are also presented.
2010 Mathematics Subject classifications:
Acknowledgements
The author would like to thank the referees for suggestions that improved this paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).