Recursive distribution estimator defined by stochastic approximation method using Bernstein polynomials. Issue 4 (2nd October 2017)

• Record Type: Journal Article
• Authors: Jmaei, Asma; Slaoui, Yousri; Dellagi, Wassima
• Is Part Of: Journal of nonparametric statistics. Volume 29:Issue 4(2017)
• Page Start: 792
• Page End: 805
• Publication Date: 2017-10-02
• Subjects: Distribution estimation -- stochastic approximation algorithm -- Bernstein polynomial; Primary: 62E20 -- 62L20; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2017.1369538
• Languages: English
• ISSNs: 1048-5252

Abstract

ABSTRACT: 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.