有差別測量誤差問題之誤差增量方法

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Title:	有差別測量誤差問題之誤差增量方法
Other Titles:	Error Augmentation in a Kind of Differential Measurement Error Problem
Authors:	黃逸輝
Contributors:	淡江大學數學學系
Date:	2010
Issue Date:	2011-07-06 00:29:24 (UTC+8)
Abstract:	自變數的測量誤差會使得迴歸模型中的參數估計有偏差，在過去已有相當多的文獻提出改正的方法或是解決的策略，幾乎所有的方法都需要假設測量誤差是無差別的，也就是說測量誤差與應變數是獨立的，測量誤差的値並不會影響應變數的分佈。然而在截斷迴歸(truncated regression)或是存活分析中的聯合模型(joint model)，測量誤差卻可能與應變數的分佈相關，我們稱這種測量誤差是有差別的，惟目前的文獻中並沒有處理這種有差別測量誤差的方法，本計劃打算提出ㄧ種新穎的概念稱之為”誤差增量”來處理此種測量誤差，這個方法無需任何新的假設，而是生成ㄧ些新的隨機誤差加入替代變數，使有差別測量誤差變成無差別測量誤差，接著構造估計方程式並且重複多次以消除生成的隨機誤差的影響作為最後的估計方程式。由初步的電腦模擬實驗結果來看，這個方法相當可行。 Measurement errors in covariates may result biased estimates in regression analysis. To reduce the bias, most correcting methods have been investigated under the surrogate condition. It assumes that measurement error makes no difference on the distribution of response variable. Such errors are called nondifferential. However, on applications of truncated regression models for count data or joint model for survival data, the number of measurements of covariates could relate with the response variable. In such cases, the surrogate condition does not hold and a differential measurement error problem emerge consequently. Unfortunately, there is no general method in literature that can deal with this problem though it arises naturally. In this project, we will exam an idea called “error augmentation” to solve this problem. It require no new assumption but generating random errors to make the differential measurement error nondifferential. A small simulation result indicates that this method promises well.
Appears in Collections:	[Graduate Institute & Department of Mathematics] Research Paper

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