Nonparametric bivariate distribution estimation using Bernstein polynomials under right censoring

被引：5

作者：

Dib, K. ^{[1
]}

Bouezmarni, T. ^{[2
]}

Belalia, M. ^{[3
]}

Kitouni, A. ^{[1
]}

机构：

[1] Univ Freres Mentouri Constantine 1, Dept Math, Constantine, Algeria

[2] Univ Sherbrooke, Dept Math, Sherbrooke, PQ, Canada

[3] Univ Windsor, Dept Math & Stat, Windsor, ON, Canada

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2021年 / 50卷 / 23期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Bernstein polynomials; bivariate distribution function; non parametric estimation; right censoring; asymptotic properties; SMOOTH ESTIMATION; DENSITY;

D O I：

10.1080/03610926.2020.1734832

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：5574 / 5584

页数：11

共 21 条

[1] Estimation of bivariate and marginal distributions with censored data [J].

Akritas, MG ;

Van Keilegom, I .

JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2003, 65 :457-471

[2] Smooth estimation of a distribution and density function on a hypercube using Bernstein polynomials for dependent random vectors [J].

Babu, GJ ;

Chaubey, YP .

STATISTICS & PROBABILITY LETTERS, 2006, 76 (09) :959-969

[3]

Babu GJ, 2002, J STAT PLAN INFER, V105, P377

[4] On the asymptotic properties of the Bernstein estimator of the multivariate distribution function [J].

Belalia, Mohamed .

STATISTICS & PROBABILITY LETTERS, 2016, 110 :249-256

[5]

Bernstein SN., 1913, Commun Soc Math Kharkow, V13, P1

[6] KAPLAN-MEIER ESTIMATE ON THE PLANE [J].

DABROWSKA, DM .

ANNALS OF STATISTICS, 1988, 16 (04) :1475-1489

[7]

Denuit M., 2006, Journal of Actuarial Practice 19932006, P5

[8]

Frees E.W., 1998, North American Actuarial Journal, V1, P1, DOI DOI 10.1080/10920277.1998.10595667

[9] Non-parametric Copula Estimation Under Bivariate Censoring [J].

Gribkova, Svetlana ;

Lopez, Olivier .

SCANDINAVIAN JOURNAL OF STATISTICS, 2015, 42 (04) :925-946

[10] Large sample behavior of the Bernstein copula estimator [J].

Janssen, Paul ;

Swanepoel, Jan ;

Veraverbeke, Noel .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2012, 142 (05) :1189-1197

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