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Simple nonparametric estimators of the bivariate survival function under random left truncation and right censoring

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  • Pao-sheng Shen

Abstract

We consider estimating the bivariate survival function when both components are subject to random left truncation and right censoring. Using the idea of Sankran and Antony (Sankhyã 69:425–447, 2007 ) in the competing risks set up, we propose two types of estimators as generalizations of the Dabrowska (Ann Stat 18:1475–1489, 1988 ) and Campbell and Földes (Nonparametric statistical inference, North-Holland, Amsterdam 1982 ) estimators. The proposed estimators are easy to implement and do not require iteration. The consistency of the proposed estimators is established. Simulation results indicate that the proposed estimators can outperform the estimators of Shen and Yan (J Stat Plan Inference 138:4041–4054, 2008 ), which require complex iteration. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • 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.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:3:p:641-659
    DOI: 10.1007/s00180-013-0455-0
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    References listed on IDEAS

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    1. Dabrowska, Dorota M., 1989. "Kaplan-Meier estimate on the plane: Weak convergence, LIL, and the bootstrap," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 308-325, May.
    2. M. J. Van Der Laan, 1997. "Nonparametric estimators of the bivariate survival function under random censoring," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 51(2), pages 178-200, July.
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