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Bootstrapping the Kaplan–Meier estimator on the whole line

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  • Dennis Dobler

    (Ulm University)

Abstract

This article is concerned with proving the consistency of Efron’s bootstrap for the Kaplan–Meier estimator on the whole support of a survival function. While previous works address the asymptotic Gaussianity of the Kaplan–Meier estimator without restricting time, we enable the construction of bootstrap-based time-simultaneous confidence bands for the whole survival function. Other practical applications include bootstrap-based confidence bands for the mean residual lifetime function or the Lorenz curve as well as confidence intervals for the Gini index. Theoretical results are complemented with a simulation study and a real data example which result in statistical recommendations.

Suggested Citation

  • Dennis Dobler, 2019. "Bootstrapping the Kaplan–Meier estimator on the whole line," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 213-246, February.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:1:d:10.1007_s10463-017-0634-9
    DOI: 10.1007/s10463-017-0634-9
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    References listed on IDEAS

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    1. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    2. R.D. Gill, 1980. "Censoring and Stochastic Integrals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 34(2), pages 124-124, June.
    3. Sze-Man Tse, 2006. "Lorenz Curve for Truncated and Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(4), pages 675-686, December.
    4. Ying, Zhiliang, 1989. "A note on the asymptotic properties of the product-limit estimator on the whole line," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 311-314, February.
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