Browsing by Subject "Nonparametric estimation"

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Open Access
Bivariate distribution and the hazard functions when a component is randomly truncated
(Elsevier, 1997-01) Gürler, Ü.
In random truncation models one observes the i.i.d. pairs (Ti≤Yi), i=1, ..., n. If Y is the variable of interest, then T is another independent variable which prevents the complete observation of Y and random left truncation occurs. Such a type of incomplete data is encountered in medical studies as well as in economy, astronomy, and insurance applications. Let (Y, Y) be a bivariate vector of random variables with joint distribution function F(y, x) and suppose the variable Y is randomly truncated from the left. In this study, nonparametric estimators for the bivariate distribution and hazard functions are considered. A nonparametric estimator for F(y, x) is proposed and an a.s. representation is obtained. This representation is used to establish the consistency and the weak convergence of the empirical process. An expression for the variance of the asymptotic distribution is presented and an estimator is proposed. Bivariate "diverse-hazard" vector is introduced which captures the individual and joint failure behaviors of the random variables in opposite "time" directions. Estimators for this vector are presented and the large sample properties are discussed. Possible applications and a moderate size simulation study are also presented. © 1997 Academic Press.
Open Access
Bivariate estimation with right-truncated data
(Taylor & Francis, 1996) Gürler, Ü.
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 iid samples of (Y, T) only if (Y ≤ T), where Y is the variable of interest and T is an independent variable that prevents the complete observation of Y. Suppose that (V, 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 iid 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.