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Asymptotic Results for Truncated-censored and Associated Data

Author

Listed:
  • Zohra Guessoum

    (University of Science and Technology Houari Boumediene (USTHB))

  • Abdelkader Tatachak

    (University of Science and Technology Houari Boumediene (USTHB))

Abstract

Left-truncation and right-censoring arise frequently when considering lifetime data. When both incompleteness conditions occur, a product-limit estimator was proposed and investigated in the independent case by Tsai et al. (Biometrika74, 883–886, 1987). In the presence of covariates, the conditional version was studied in the α-mixing setting by Liang et al. (Test21, 790–810, 2012). Our objective in the present paper is to derive strong uniform consistency rates for the cumulative hazard and the product-limit estimates when the lifetime observations form an associated sequence. Then, as an application we derive a strong uniform consistency rate for the kernel estimator of the hazard rate function considered by Uzunoḡullari and Wang (Biometrika79, 297–310, 1992) in the iid case.

Suggested Citation

  • Zohra Guessoum & Abdelkader Tatachak, 2020. "Asymptotic Results for Truncated-censored and Associated Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 142-164, May.
    • Handle: RePEc:spr:sankhb:v:82:y:2020:i:1:d:10.1007_s13571-018-00185-4
    DOI: 10.1007/s13571-018-00185-4
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    References listed on IDEAS

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    5. Guessoum, Zohra & Ould Saïd, Elias & Sadki, Ourida & Tatachak, Abdelkader, 2012. "A note on the Lynden-Bell estimator under association," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1994-2000.
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