Nonparametric bivariate distribution estimation using Bernstein polynomials under right censoring

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.

Keywords:

• Bernstein polynomials
• bivariate distribution function
• non parametric estimation
• right censoring
• asymptotic properties

Additional information

Funding

T. Bouezmarni gratefully acknowledges the research support of the Natural Sciences and Engineering Research Council of Canada (NSERC: 402521-2013) and Fonds de recherche du Québec - Nature et technologies (FRQNT: 2016-NC-190250).