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Kaplan-Meier estimate on the plane: Weak convergence, LIL, and the bootstrap


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  • Dabrowska, Dorota M.
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    We consider estimation of the bivariate survival function F(s,t) under bivariate random right censoring. It is shown that the bivariate product integral estimator can be written as , where is a sum of mean zero iid processes and is a remainder term of order O((n-1logn)1/2 (n-1log logn)1/8) a.s. Using this representation we establish weak convergence of as well as the law of iterated logarithm. Similar results are obtained for the bootstrap version of .

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 29 (1989)
    Issue (Month): 2 (May)
    Pages: 308-325

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    Handle: RePEc:eee:jmvana:v:29:y:1989:i:2:p:308-325

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    Keywords: bivariate censored data bivariate product integral estimate;


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    Cited by:
    1. Kouros Owzar & Pranab Kumar Sen, 2003. "Copulas: concepts and novel applications," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 323-353.
    2. Chen, Xiaohong & Fan, Yanqin & Pouzo, Demian & Ying, Zhiliang, 2010. "Estimation and model selection of semiparametric multivariate survival functions under general censorship," Journal of Econometrics, Elsevier, vol. 157(1), pages 129-142, July.
    3. Fermanian, Jean-David, 1997. "Multivariate Hazard Rates under Random Censorship," Journal of Multivariate Analysis, Elsevier, vol. 62(2), pages 273-309, August.
    4. Pao-sheng Shen, 2014. "Simple nonparametric estimators of the bivariate survival function under random left truncation and right censoring," Computational Statistics, Springer, vol. 29(3), pages 641-659, June.
    5. Xiaohong Chen & Yanqin Fan & Demian Pouzo & Zhiliang Ying, 2008. "Estimation and Model Selection of Semiparametric Multivariate Survival Functions under General Censorship," Cowles Foundation Discussion Papers 1683, Cowles Foundation for Research in Economics, Yale University.
    6. Wang, Qi-Hua, 2000. "Moment and probability inequalities for the bivariate product-limit estimator," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 1-12, January.


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