Nonparametric bivariate distribution estimation using Bernstein polynomials under right censoring. Issue 23 (2nd December 2021)

• Record Type: Journal Article
• Authors: Dib, K.; Bouezmarni, T.; Belalia, M.; Kitouni, A.
• Is Part Of: Communications in statistics. Volume 50:Issue 23(2021)
• Page Start: 5574
• Page End: 5584
• Publication Date: 2021-12-02
• Subjects: Bernstein polynomials -- bivariate distribution function -- non parametric estimation -- right censoring -- asymptotic properties; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2020.1734832
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: The paper deals with non parametric estimation of the joint distribution function of two random variables X and Y . Especially, we consider the case when one of the two variables, says Y, is subject to right censoring. The newly proposed estimator is built using Bernstein polynomials. The asymptotic properties of this estimator such as, bias, variance and normality are provided. Also, we prove the strong uniform convergence. The proposed estimator is applied to analyze the Loss-ALAE dataset from insurance.