Open Access Open Access  Restricted Access Subscription or Fee Access

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

Fatma Ben Khadher, Yousri Slaoui

Abstract



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.

Keywords


Stochastic approximation algorithm; recursive distribution estimator; Mixing Data; Bandwidth selection; Asymptotic normality.

Full Text:

PDF


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.