A Bernstein polynomial approach to the estimation of a distribution function and quantiles under censorship model

Abstract

In this article, we investigate various asymptotic properties (bias, variance, mean squared error, mean integrated squared error, asymptotic normality, uniform strong consistency) for Bernstein estimators of quantiles and cumulative distribution functions when the variable of interest is subject to random right-censored. In this work, we extend to the case of censored data the results of Leblanc and Babu, Canty and Chaubey. A simulation study is considered to show the performance of the proposed estimator.

Keywords:

• Bernstein estimators
• distribution function estimation
• quantile function estimation
• censored data
• asymptotic properties

AMS Subject Classification:

• Primary: 62N01
• 62N02
• Secondary: 62G08
• 62G20

Acknowledgments

The author is indebted to the Editor-in-Chief of Communications in Statistics Theory and Methods, the associate Editor and the two anonymous reviewers for their very valuable comments and suggestions which led to a considerable improvement of the manuscript.