The stochastic approximation method for estimation of a distribution function

We apply the stochastic approximation method to construct a large class of recursive kernel estimators of a distribution function. We study the properties of these estimators and compare them with Nadaraya’s distribution estimator. It turns out that, with an adequate choice of the stepsize of the proposed algorithm, the MWISE (Mean Weighted Integrated Squared Error) of the proposed estimator is smaller than that of Nadaraya’s estimator. We corroborate these theoretical results by simulations and a real dataset.