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Law of the Logarithm for Density and Hazard Rate Estimation for Censored Data

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  • Xiang, X. J.

Abstract

In this note, we establish law of the logarithm for kernel-type density and hazard rate estimators based on censored data. These results are applied to get optimal bandwidths with respect to strong uniform consistency.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:49:y:1994:i:2:p:278-286
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    Cited by:

    1. 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.
    2. Mokkadem, Abdelkader & Pelletier, Mariane, 2021. "A compact law of the iterated logarithm for online estimator of hazard rate under random censoring," Statistics & Probability Letters, Elsevier, vol. 178(C).
    3. Talamakrouni, Majda & Van Keilegom, Ingrid & El Ghouch, Anouar, 2016. "Parametrically guided nonparametric density and hazard estimation with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 308-323.
    4. Einmahl, J.H.J. & Deheuvels, P., 2000. "Functional limit laws for the increments of Kaplan-Meier product-limit processes and applications," Other publications TiSEM ac9bbdc0-62f8-4b48-9a84-1, Tilburg University, School of Economics and Management.
    5. Junshan Shen & Shuyuan He, 2008. "Empirical likelihood confidence intervals for hazard and density functions under right censorship," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 575-589, September.
    6. Fermanian, Jean-David, 1997. "Multivariate Hazard Rates under Random Censorship," Journal of Multivariate Analysis, Elsevier, vol. 62(2), pages 273-309, August.
    7. Liang, Han-Ying & de Ua-lvarez, Jacobo, 2009. "A Berry-Esseen type bound in kernel density estimation for strong mixing censored samples," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1219-1231, July.

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