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Non‐parametric Estimation for the Location of a Change‐point in an Otherwise Smooth Hazard Function under Random Censoring

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  • Anestis Antoniadis
  • Irene Gijbels
  • Brenda Macgibbon

Abstract

A non‐parametric wavelet based estimator is proposed for the location of a change‐point in an otherwise smooth hazard function under non‐informative random right censoring. The proposed estimator is based on wavelet coefficients differences via an appropriate parametrization of the time‐frequency plane. The study of the estimator is facilitated by the strong representation theorem for the Kaplan–Meier estimator established by Lo and Singh (1986). The performance of the estimator is checked via simulations and two real examples conclude the paper.

Suggested Citation

  • Anestis Antoniadis & Irene Gijbels & Brenda Macgibbon, 2000. "Non‐parametric Estimation for the Location of a Change‐point in an Otherwise Smooth Hazard Function under Random Censoring," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(3), pages 501-519, September.
    • Handle: RePEc:bla:scjsta:v:27:y:2000:i:3:p:501-519
    DOI: 10.1111/1467-9469.00203
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    Cited by:

    1. Altun, Mustafa & Comert, Salih Vehbi, 2016. "A change-point based reliability prediction model using field return data," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 175-184.
    2. Alessandra R. Brazzale & Helmut Küchenhoff & Stefanie Krügel & Tobias S. Schiergens & Heiko Trentzsch & Wolfgang Hartl, 2019. "Nonparametric change point estimation for survival distributions with a partially constant hazard rate," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(2), pages 301-321, April.
    3. Angers, Jean-Francois & MacGibbon, Brenda, 2013. "Hazard function estimation with nonnegative “wavelets”," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 969-978.
    4. Jingle Wang & Ming Zheng, 2012. "Wavelet detection of change points in hazard rate models with censored dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 765-781.
    5. Nora M. Villanueva & Marta Sestelo & Miguel M. Fonseca & Javier Roca-Pardiñas, 2023. "seq2R: An R Package to Detect Change Points in DNA Sequences," Mathematics, MDPI, vol. 11(10), pages 1-20, May.

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