An inverse-probability-weighted approach to estimation of truncation probability and censoring distribution

• Main Authors: Chun-Nan Chen, 陳俊男
• Other Authors: Pao-Sheng Shen
• Format: Others
• Language: en_US
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/43856901881805698231

碩士 === 靜宜大學 === 應用數學研究所 === 93 === Let (Ui* ,Ci*, Vi* ) be i.i.d. random vectors such that (Ci*, Vi*) is independent of Ui* and P(Ci*≧Vi* ) = 1. Let F, Q and G denote the common distribution function of Ui* ,Ci* and Vi* , respectively. For left-truncated and right-censored data, one can observe nothing if Ui*< Vi* and observe (Xi *; δi*), with Xi *= min(Ui*; Ci*) andδi* = I[Ui*≦Ci*], if Ui*≧ Vi*. Two questions of interest are how to estimate the truncation probabilityα = P(Ui* ≧Vi* ) and the censoring distribution Q. Under the constraint that P(Ci*≧Vi* ) = 1, Wang (1991) suggested estimating α byα = ∫[1-Fn(s-)]dGn(s), where Fn and Gn are nonparametric maximum likelihood estimate (NPMLE) of the distributions F and G, respectively. In this note, using an inverse-probability-weighted (IPW) approach, we obtain an alternative representation α^n for α . With this, good behaviors ofα^n, Fn and Gn induce nice properties in the IPW estimator of q (denoted by Q^e). Simulation study shows that both Q^e and α work satisfactorily for moderate sample size.