Jackknife methods for truncated data

• Main Authors: Meng-Fu Shih, 施孟甫
• Other Authors: Pao-Sheng Shen
• Format: Others
• Language: en_US
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/03127270794409125599

碩士 === 東海大學 === 統計學系 === 88 === Let $X$ and $Y$ be two independent positive random variables with survival functions $\bar F$ and $\bar G$, respectively. Under random truncation, $X$ and $Y$ are both observable only when $X\ge Y$. The nonparametric MLE of $\bar F (x)$, $\bar F_n (x) =1-F_n (x)= 1-\prod_{z\le x} [1-d\Lambda_n (z)]$, was derived by Lynden-Bell (1971), where $\Lambda_n (z)$ is the estimated cumulative hazard function. In this note, we derive an explicit formula for the delete-d jackknife estimate of $\Lambda_{n} (z)$. From this it is demonstrated that jackknifing may lead to a reduction of the bias. Besides, it is shown that the delete-1 jackknife variance estimator of $\bar F_n (x)$ consistently estimates the limit variance.