Efficiency behaviour of kernel-smoothed kernel distribution function estimators

Paul Janssen; Jan W. H. Swanepoel; Noël Veraverbeke

doi:10.37920/sasj.2020.54.1.2

Paul Janssen Hasselt University, Center for Statistics, Diepenbeek, Belgium
Jan W. H. Swanepoel North-West University, Potchefstroom, South Africa
Noël Veraverbeke Hasselt University, Center for Statistics, Diepenbeek, Belgium; North-West University, Potchefstroom, South Africa

DOI: https://doi.org/10.37920/sasj.2020.54.1.2

Keywords: Asymptotic mean integrated squared error, Kernel distribution function estimator, Kernel efficiency

Abstract

The asymptotic mean integrated squared error (AMISE) and the kernel efficiency (KE) of kernel distribution function estimators are well studied. In this note we define new nonparametric distribution function estimators by kernel-smoothing an initial kernel distribution function estimator. We show that, under certain conditions, the AMISE and the KE can be improved. A concrete example and a Monte Carlo simulation are worked out for illustration.