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政大機構典藏 > 商學院 > 統計學系 > 學位論文 > Item 140.119/85146

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/85146

Title:	變數轉換之離群值偵測 Detection of Outliers with Data Transformation
Authors:	吳秉勳 Wu, David
Contributors:	鄭宗記吳秉勳 David Wu
Keywords:	容離值最小中位數穩健迴歸估計值遮蔽效應最小體積橢圓體估計值 Mahalanobis 距離分數統計量鐘乳石圖步進搜尋演算法 Breakdown Point Least Median Square (LMS) Estimator The Masking Effect Minimum Volume Ellipsoid (MVE) Estimator Mahalanobis Distance Score Statistic Stalactite Plot The Forward Search Algorithm
Date:	2001
Issue Date:	2016-04-15 16:10:25 (UTC+8)
Abstract:	在迴歸分析中，當資料中存在很多離群值時，偵測的工作變得非常不容易。在此狀況下，我們無法使用傳統的殘差分析正確地偵測出其是否存在，此現象稱為遮蔽效應(The Masking Effect)。而為了避免此效應的發生，我們利用最小中位數穩健迴歸估計值(Least Median Squares Estimator)正確地找出這些群集離群值，此估計值擁有最大即50﹪的容離值 (Breakdown point)。在這篇論文中，用來求出最小中位數穩健迴歸估計值的演算法稱為步進搜尋演算法 (the Forward Search Algorithm)。結果顯示，我們可以利用此演算法得到的穩健迴歸估計值，很快並有效率的找出資料中的群集離群值；另外，更進一步的結果顯示，我們只需從資料中隨機選取一百次子集，並進行步進搜尋，即可得到概似的穩健迴歸估計值並正確的找出那些群集離群值。最後，我們利用鐘乳石圖(Stalactite Plot)列出所有被偵測到的離群值。 Detecting regression outliers is not trivial when there are many of them. The methods of using classical diagnostic plots sometimes fail to detect them. This phenomenon is known as the masking effect. To avoid this, we propose to find out those multiple outliers by using a highly robust regression estimator called the least median squares (LMS) estimator which has maximal breakdown point. The algorithm in search of the LMS estimator is called the forward search algorithm. The estimator found by the forward search is shown to lead to the rapid detection of multiple outliers. Furthermore, the result reveals that 100 repeats of a simple forward search from a random starting subset are shown to provide sufficiently robust parameter estimators to reveal multiple outliers. Finally, those detected outliers are exhibited by the stalactite plot that shows greatly stable pattern of them.
Description:	碩士國立政治大學統計學系 87354011
Source URI:	http://thesis.lib.nccu.edu.tw/record/#A2002001359
Data Type:	thesis
Appears in Collections:	[統計學系] 學位論文

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