Nonparametric bivariate distribution estimation using Bernstein polynomials under right censoring

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...

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Bibliographic Details
Published inCommunications in statistics. Theory and methods Vol. 50; no. 23; pp. 5574 - 5584
Main Authors Dib, K., Bouezmarni, T., Belalia, M., Kitouni, A.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.12.2021
Taylor & Francis Ltd
Subjects
Asymptotic properties
Bernstein polynomials
Bivariate analysis
bivariate distribution function
Distribution functions
Mathematical analysis
non parametric estimation
Nonparametric statistics
Normality
Parameter estimation
Polynomials
Random variables
right censoring
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2020.1734832