Bernoulli

  • Bernoulli
  • Volume 2, Number 2 (1996), 183-198.

Some asymptotic results for kernel density estimation under random censorship

Biao Zhang

Full-text: Open access

Abstract

Random censored data consist of i.i.d. pairs of observations (Xii), i=1,...,n. If δi=0, Xi denotes a censored observation, and if δi=1, Xi denotes a survival time, which is the variable of interest. In this paper, we apply the martingale method for counting processes to study asymptotic properties for the kernel estimator of the density function of the survival times. We also derive an asymptotic expression for the mean integrated square error of the kernel density estimator, which can be used to obtain an asymptotically optimal bandwidth.

Article information

Source
Bernoulli, Volume 2, Number 2 (1996), 183-198.

Dates
First available in Project Euclid: 31 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1193839223

Digital Object Identifier
doi:10.3150/bj/1193839223

Mathematical Reviews number (MathSciNet)
MR1410137

Zentralblatt MATH identifier
0858.62034

Keywords
bandwidth counting process martingale Kaplan-Meier estimator mean integrated square error

Citation

Zhang, Biao. Some asymptotic results for kernel density estimation under random censorship. Bernoulli 2 (1996), no. 2, 183--198. doi:10.3150/bj/1193839223. https://projecteuclid.org/euclid.bj/1193839223


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