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A compact law of the iterated logarithm for online estimator of hazard rate under random censoring

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  • Mokkadem, Abdelkader
  • Pelletier, Mariane

Abstract

Douma et al. (2018) introduced a recursive kernel estimator of the hazard function in the framework of independent rightly censored data, and studied its weak convergence rate, without giving any result on its strong behavior. The aim of this paper is to establish a compact law of the iterated logarithm for this estimator, which requires an approach in the proof totally different from that used in Douma et al. (2018).

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:178:y:2021:i:c:s0167715221001486
    DOI: 10.1016/j.spl.2021.109186
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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. Godichon-Baggioni, Antoine, 2016. "Estimating the geometric median in Hilbert spaces with stochastic gradient algorithms: Lp and almost sure rates of convergence," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 209-222.
    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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