Kernel estimation of a distribution function

The most commonly used nonparametric estimation of a distribution function F is an empirical distribution function F_n. But F_n is a step function even in case that F is continuous. Nadaraya (1964) proposed a smooth non-parametric alternative to F_n, namely, kernel distribution estimator. This estimator is obtained by integrating the well known Rosenblatt-Parzen kernel density estimate (2.2). More generally, having a nonparametric estimate of f one can obtain a nonparametric estimate of F by integrating …