Recursive distribution estimator defined by stochastic approximation method using Bernstein polynomials

摘要

We propose a recursive distribution estimator using Robbins-Monro's algorithm and Bernstein polynomials. We study the properties of the recursive estimator, as a competitor of Vitale's distribution estimator. We show that, with optimal parameters, our proposal dominates Vitale's estimator in terms of the mean integrated squared error. Finally, we confirm theoretical result throught a simulation study.