Problems arising from jackknifing the estimate of a Kaplan-Meier integral

✍ Scribed by Pao-Sheng Shen

• Book ID: 104302920
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 364 KB
• Volume: 40
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(98)00135-7

✦ Synopsis

Stute and Wang (1994)

considered the problem of estimating the integral Sr= f q~dF, based on a possibly censored sample from a distribution F, where 4) is an F-integrable function. They proposed a Kaplan-Meier integral S.~ to approx-"~ ^6 differs from S~ only when the imate S ~ and derived an explicit formula for the delete-1 jackknife estimate S,,~l ). Sn~])

largest observation, X~.), is not censored (6~n)= 1) and next-to-the-largest observation, X~.-l), is censored (6~.-1)= 0). In this note, it will be pointed out that when X~.) is censored (6~.) = 0) S~ is based on a defective distribution, and therefore n(I) S~) can badly underestimate S 6. We derive an explicit formula for the delete-2 jackknife estimate S~z)" However, on comparing the expressions of S~I) and S.~2), their difference is negligible. To improve the performance of S.~l I and S~2), we propose a modified estimator S~ according to Efron (1980). Simulation results demonstrate that S~ is much less biased than S~f~) and S~2)'