The Annals of Statistics

Some Asymptotic Properties of Kernel Estimators of a Density Function in Case of Censored Data

Jan Mielniczuk

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Abstract

The kernel estimator is a widely used tool for the estimation of a density function. In this paper its adaptation to censored data using the Kaplan-Meier estimator is considered. Asymptotic properties of four estimators, arising naturally as a result of considering various types of bandwidths, are investigated. In particular we show that (i) both proposed estimators stemming from the nearest neighbor estimator have censoring-free variances and (ii) one of them is pointwise mean consistent.

Article information

Source
Ann. Statist., Volume 14, Number 2 (1986), 766-773.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349954

Digital Object Identifier
doi:10.1214/aos/1176349954

Mathematical Reviews number (MathSciNet)
MR840530

Zentralblatt MATH identifier
0603.62047

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 60F15: Strong theorems

Keywords
Censored data density estimator $k$ nearest neighbor estimator Kaplan-Meier estimator kernel random censorship model

Citation

Mielniczuk, Jan. Some Asymptotic Properties of Kernel Estimators of a Density Function in Case of Censored Data. Ann. Statist. 14 (1986), no. 2, 766--773. doi:10.1214/aos/1176349954. https://projecteuclid.org/euclid.aos/1176349954


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