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

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, <CitationRef CitationID="CR16">2007</CitationRef>) in the competing risks set up, we propose two types of estimators as generalizations of the Dabrowska (Ann Stat 18:1475–1489, <CitationRef CitationID="CR2">1988</CitationRef>) and Campbell and Földes (Nonparametric statistical inference, North-Holland, Amsterdam <CitationRef CitationID="CR1">1982</CitationRef>) 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, <CitationRef CitationID="CR18">2008</CitationRef>), which require complex iteration. Copyright Springer-Verlag Berlin Heidelberg 2014