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Rate of strong consistency for nonparametric estimators based on twice censored data

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  • Kitouni, Abderrahim
  • Boukeloua, Mohamed
  • Messaci, Fatiha

Abstract

We establish the uniform almost complete convergence, with rate, for estimators of both the cumulative hazard and the survival functions when the data are subject to twice censoring. Then, we derive similar convergence results for kernel type estimators of the density and the failure rate.

Suggested Citation

  • Kitouni, Abderrahim & Boukeloua, Mohamed & Messaci, Fatiha, 2015. "Rate of strong consistency for nonparametric estimators based on twice censored data," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 255-261.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:255-261
    DOI: 10.1016/j.spl.2014.10.005
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    References listed on IDEAS

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    1. Xiang, X. J., 1994. "Law of the Logarithm for Density and Hazard Rate Estimation for Censored Data," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 278-286, May.
    2. Messaci, Fatiha & Nemouchi, Nahima, 2011. "A law of the iterated logarithm for the product limit estimator with doubly censored data," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1241-1244, August.
    3. 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.
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    Cited by:

    1. Boukeloua, Mohamed, 2015. "Rates of mean square convergence of density and failure rate estimators under twice censoring," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 121-128.
    2. Nour El Houda Rouabah & Nahima Nemouchi & Fatiha Messaci, 2019. "A rate of consistency for nonparametric estimators of the distribution function based on censored dependent data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 259-280, June.

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