Nonparametric estimation of the conditional survival function with double smoothing

Abstract

In this paper, a conditional survival function estimator for censored data is studied. It is based on a double smoothing technique: both the covariate and the variable of interest (usually, the time) are smoothed. Asymptotic expressions for the bias and the variance and the asymptotic normality of the smoothed survival estimator derived from Beran's estimator are found. A simulation study shows the performance of the smoothed Beran's estimator of the conditional survival function and compares it with the smoothed one only in the covariate. The influence of the two smoothing parameters involved in both estimators is also studied.

Keywords:

• Censored data
• conditional survival function
• nonparametric estimator
• survival analysis

2000 Mathematics Subject Classifications:

• 62N02
• 62G05

Acknowledgments

The authors would like to thank an anonymous Associate Editor and two anonymous reviewers for their helpful comments that have been of great help to improve this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research has been supported by MINECO Grant MTM2017-82724-R, and by the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2016-015, ED431C-2020-14 and Centro Singular de Investigación de Galicia ED431G 2019/01), all of them through the ERDF.