The Stochastic Approximation Method for Estimation of a Distribution Function under α-mixing condition

In this article, we extend the work of Slaoui (2014b) [The stochastic approximation method for the estimation of a distribution function. Math. Methods Statist., 23, 306–325] to the case of α-mixing data. Then, we study the properties of these estimators and compare them with Nadaraya’s non recursive distribution estimator. We show that, using some optimal parameters, the recursive estimators allowed us to obtain quite better results compared to the non recursive distribution estimator under α-mixing condition in terms of estimation error. We establish the central limit theorem and the uniform convergence for the proposed estimators under some mild conditions. Finally, we corroborate these theoretical results through a few simulations.