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Title: Non-parametric estimators for estimating bivariate survival function under randomly censored and truncated data Authors:  Marialuisa Restaino - University of Salerno (Italy) [presenting]
Hongsheng Dai - University of Essex (United Kingdom)
Huan Wang - The University of Dundee (United Kingdom)
Abstract: In bivariate survival analysis it is common to dealt with incomplete information of the data, due to random censoring and random truncation. Such kind of data occurs in many research areas, such as medicine, economics, insurance and social sciences. Most existing research papers focused on bivariate survival analysis when components are either censoring or truncation or where one component is censored and truncated, but the other one is fully observed. Bivariate survival function estimation when both components are censored and truncated has received considerable attention recently. These methods, however, used an iterative computing method which is computationally heavy. Some authors proposed an estimator based on a polar coordinate transformation, which does not require iterative calculations and its large sample properties are established. Starting from their paper, we extend their methods to a class of estimators, based on different data transformations. In particular assuming that the components are both random truncation and random censoring, we propose a class of nonparametric estimators for the bivariate survival function. The proposed class of nonparametric estimators uses such parametric information via a data transformation approach and thus provides more accurate estimates than existing methods without using such information. The proposed method is also justified via a simulation study and an application on an economic data set.