On Incomplete Data And the Bias-Corrected Jackknife Estimate

CNU IR > Chna Nan Annual Bulletin > Vol.24 (1998) > Item 310902800/22762

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Title:	On Incomplete Data And the Bias-Corrected Jackknife Estimate 不完全資料與Jackknife偏差校正估計量的關係
Authors:	Wen-Sz Chiue Bih-Sheue Shieh
Contributors:	化妝品應用與管理學系資訊管理學系
Keywords:	Emulsifier Angel rice cake Volume index Quality 偏差校正 Jackknife Kaplan-Meier 估計量 Quenouille's方法
Date:	1998
Issue Date:	2010-05-11 14:09:19 (UTC+8)
Abstract:	We derive an explicit formula of S( n),where1-n is the Kaplan-Meier estimate of the incom-plete data X1,…,Xn,where X1,…,Xn are identical and independent random variables with common unknown distribution F and S is a given integral function.Since the X's are incomplete,S(n) is typically biased.Quenouille (1965) invented a method to estimate the bias nonparametrically and then to replace S(n) by a bias-corrected estimate： the jackknife.From this, the relationship between the bias-corrected jackknife estimate of S(F) and the observation data of X1,…,Xn is pointed out. 設X1,X2，…，Xn，為一獨立且具有相同分配函數F ( F為未知)的隨機變數樣本，設S為一已知的統計函數，我們想估計S(F)。當X1,X2，…，Xn可完全觀察到時，最典型的方法是用S(F,)估計S(F)，此處Fn為X1,X2，…，Xn的經驗分配函數。當S非線性時， S(Fn)為一偏的估計量，因此 ; Quenouille於1956年提出用Jackknife的方法估t此偏差量，稱為Quenouille偏差估計量，並導出一個偏差校正估計量，此法有效的降低估S (F)的偏差量。當X1,X2，…，Xn的資料不能完全被觀察到時，一般用S(Fn)估S(F)，此處l-F n為X1,X2，…，Xn，的Kaplan-Me ier估計量。因為X1,X2，…，Xn的資料不完全，即使S為一線性函數，S(Fn)仍為一偏的估計量。此篇論文，我們利用Kaplan-Meier估計量及Jackknife估計量的定義，準確地算出S(Fn)的Quenouille偏差估計量，並導出出S (F)的Jackknife偏差校正估計量與觀察值X1,X2,，…，Xn，的關係。
Relation:	嘉南學報 24期 : p.126-132
Appears in Collections:	[Chna Nan Annual Bulletin] Vol.24 (1998) [Dept. of Cosmetic Science and institute of cosmetic science] Periodical Articles [Dept. of Information Management] Periodical Articles

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