Data-based bandwidth selection for kernel smoothing of empirical distribution functions

Abstract This paper makes three contributions to the estimation of distribution functions by smoothed empirical distribution functions based on kernel smoothing. First, we provide some theoretical evidence that the order of the kernel plays a minor role. Second, we propose two new data-based bandwidth selectors that are easy to implement, analyse them, and compare them with related approaches known from the literature. Our numerical experiments show that our proposals perform very well and that one of them is particularly strong w.r.t. the integrated squared error (ISE) in direct comparison with the empirical distribution function. Third, we prove strong consistency of the smoothed empirical distribution function in the case where the kernel smoothing is based on our data-based bandwidth selectors.