(An) estimation of location-shift parameter under random truncation

Abstract

One source of data for the induction distribution of AIDS arises from persons infected by the AIDS virus from contaminated blood transfusions. Analyses of these data are complicated because the number of individuals infected by transfusion is unknown; information is available only for those who are infected and develop AIDS within a certain chronologic time interval. This kind of biased sampling is called truncation. Truncation can be a problem in many areas like economics, astronomy and medical research. One of statistical problems is making inferences about a location-shift parameter under two sample location-shift model. Unfortunately, there is no suggested estimator of location-shift parameter under random truncation. We can simply consider the difference of each medians as an estimator and develop nonparametric methods for estimating the location-shift parameter. This estimator is based on the quantile function( Park & Park 1993). Consistency and weak convergence of the proposed estimator is proved and a simulation study comparing simple difference of medians and the proposed estimator is presented. Finally, an application of the suggested estimator is presented for transfusion-related AIDS (TR-AIDS) data on the incubation time.