The Nonparametric MLE As an Inverse-Probability-of Truncation Weighted Average

非參數最大估計值表示成以截取機率爲權數之平均值

沈葆聖(Pao-Sheng Shen)

《東海管理評論》 4卷1期 (2002/07) Pp. 17-25

https://doi.org/10.29724/TMR.200207.0002

摘要

對於隨機設限資料，Satten和Datta (2001)證明Kaplan-Meier估計值可以表示成以設限時間機率分配為權數的加權平均值。本文中，我們證明截取資料下，Lynden-Bell(1971)所提出的product-limit估計值亦可表示成以截取時間機率分配為權數的加權平均值。

關鍵字

Product-Limit估計值 ； 隨機截取

並列摘要

For randomly censored data, Satten and Datta (2001) showed that the Kaplan-Meier estimator can be expressed as an inverse-probability-of censoring weighted estimator. In this article, it is shown that the truncation product-limit estimate, first introduced by Lynden-Bell(1971), can also be expressed as an inverse-probability-of truncation weighted average, where the weights are related to the distribution function of truncation variables.

並列關鍵字

Product-Limit Estimator ； Random Truncation

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