Efficiency Behaviour of Kernel-Smoothed Kernel Distribution Function Estimators

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 non-parametric 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.