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Asymptotic-based bandwidth selection for the presmoothed density estimator with censored data

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  • Maria Jácome
  • Ricardo Cao

Abstract

This paper is concerned with the problem of selecting a suitable bandwidth for the presmoothed density estimator from right-censored data. An asymptotic expression for the mean integrated squared error (MISE) of this estimator is given, and the smoothing parameters minimising it are proved to be consistent approximations of the MISE bandwidths. As a consequence, a bandwidth selector based on plug-in ideas is introduced. We also present a bootstrap bandwidth selector. The performance of both methods is investigated in a simulation study, in which the Kaplan–Meier kernel density estimator has been taken as a relevant competitor.

Suggested Citation

  • Maria Jácome & Ricardo Cao, 2008. "Asymptotic-based bandwidth selection for the presmoothed density estimator with censored data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(6), pages 483-506.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:6:p:483-506
    DOI: 10.1080/10485250802280226
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    References listed on IDEAS

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    1. C. Sánchez-Sellero & W. González-Manteiga & R. Cao, 1999. "Bandwidth Selection in Density Estimation with Truncated and Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(1), pages 51-70, March.
    2. Diehl, Sabine & Stute, Winfried, 1988. "Kernel density and hazard function estimation in the presence of censoring," Journal of Multivariate Analysis, Elsevier, vol. 25(2), pages 299-310, May.
    3. Cao, R., 1993. "Bootstrapping the Mean Integrated Squared Error," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 137-160, April.
    4. Cao, Ricardo & Cuevas, Antonio & Gonzalez Manteiga, Wensceslao, 1994. "A comparative study of several smoothing methods in density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 17(2), pages 153-176, February.
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