The Annals of Statistics

Asymptotically Optimal Bandwidth Selection for Kernel Density Estimators from Randomly Right-Censored Samples

J. S. Marron and W. J. Padgett

Full-text: Open access

Abstract

This paper makes two important contributions to the theory of bandwidth selection for kernel density estimators under right censorship. First, an asymptotic representation of the integrated squared error into easily understood variance and squared bias components is given. Second, it is shown that if the bandwidth is chosen by the data-based method of least-squares cross-validation, then it is asymptotically optimal in a compelling sense. A by-product of the first part is an interesting comparison of the two most popular kernel estimators.

Article information

Source
Ann. Statist., Volume 15, Number 4 (1987), 1520-1535.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350607

Digital Object Identifier
doi:10.1214/aos/1176350607

Mathematical Reviews number (MathSciNet)
MR913571

Zentralblatt MATH identifier
0657.62038

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62G20: Asymptotic properties

Keywords
Nonparametric density estimation optimal bandwidth random censorship smoothing parameter cross-validation

Citation

Marron, J. S.; Padgett, W. J. Asymptotically Optimal Bandwidth Selection for Kernel Density Estimators from Randomly Right-Censored Samples. Ann. Statist. 15 (1987), no. 4, 1520--1535. doi:10.1214/aos/1176350607. https://projecteuclid.org/euclid.aos/1176350607


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