Bivariate estimation with right-truncated data
(1996) Journal of the American Statistical Association — Vol. 91, n° 435, p. 1152-1165 (1996)
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- Bivariate estimation with survival data has received considerable attention recently; however, most of the work has focused on random censoring models. Another common feature of survival data, random truncation, is considered in this study. Truncated data may arise if the time origin of the events under study precedes the observation period. In a random right-truncation model, one observes the lid samples of (Y, T) only if (Y less than or equal to T), where Y is the variable of interest and T is an independent variable that prevents the complete observation of Y. Suppose that (Y, X) is a bivariate vector of random variables, where Y is subject to right truncation. In this study the bivariate reverse-hazard vector is introduced, and a nonparametric estimator is suggested. An estimator for the bivariate survival function is also proposed. Weak convergence and strong consistency of this estimator are established via a representation by lid variables. An expression for the limiting covariance function is provided, and an estimator for the limiting variance is presented. Alternative methods for estimating the bivariate distribution function are discussed. Obtaining large-sample results for the bivariate distribution functions present more technical difficulties, and thus their performances are compared via simulation results. Finally, an application of the suggested estimators is presented for transfusion-related AIDS (TR-AIDS) data on the incubation time.
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Gurler, U. (1996). Bivariate estimation with right-truncated data. Journal of the American Statistical Association, 91(435), 1152-1165. https://doi.org/10.2307/2291734 (Original work published 1996)