On testing independence with right truncated data

Inference with bivariate data gained considerable interest recently, See eg.[1],[10],[12]. All of these studies howrver consider estimation of the bivariate distribution function under various bivariate censoring models. Recently (:iirler[7,8] considered estimation of the bivariate distribution and the hazard functions under trunc.atlon/censoring models. The purpose of this study is to investigate procedures for testing the independence of I hc components of the bivariate vector for truncated data. To this end, further properties of the bivariate functrouals introduced in GiirleQ] are elaborated. Two alternative methods for hypothesis testing are suggested aud some large sample properties are derived. The procedures suggested in this paper are applicable to left/right. truncated and left truncated right censored data. However to keep the presentation simple we ~~oufinr t.hr discussion to the right truncated case. Also, to avoid technicalities, it is assumed that all the univariat.e and the bivariate distribution functions are absolutely continuous admitting densities.