题名

線性迴歸模型的影響測度比較

并列篇名

Comparisons of the Influence Measures in Linear Regression Models

作者

黃郁芬(Yu-Fen Huang);黃治興(Chih-Hsiang Hwang)

关键词

影響函數 ; 局部影響函數 ; 線性迴歸 ; 擾動 ; Influence function ; local influence ; linear regression ; perturbation

期刊名称

中國統計學報

卷期/出版年月

51卷2期(2013 / 06 / 01)

页次

225 - 245

内容语文

英文

中文摘要

在統計分析資料的方法中,線性迴歸分析是很重要的分析工具之一,而此方法通常也和模型配適的近似程度有關。而不正常的觀測值會劇烈的影響分析的結果,因此不正常的觀測值需要被偵測出來。在本文中,我們研究及比較調查三種不同的統計方法如何檢測在線性迴規模型中具有影響力的觀測值。這三種方法分別是由Hample(1974)、Cook(1986)以及Peña(2005)所提出的。此外,在本文中提供了一筆模擬的資料與兩筆真實資料去闡述這三種方法的結果。

英文摘要

Linear regression is one of the most important tools to analyze the data, and it usually involves some degree of approximation. The unusual observations can greatly influence the results of the analysis. Therefore, the unusual observations need to be detected. In this paper, we restrict ourselves to study and investigate three different approaches on the detection of influential observations in linear regression models. These three methods were proposed by Hampel (1974), Cook (1986) and Peña (2005), respectively. One simulated data and two real data examples are provided to illustrate the results of these three approaches.

主题分类 基礎與應用科學 > 統計
参考文献
  1. Cook, R. D.(1986).Assessment of local influence.Journal of the Royal Statistical Society Series B,48,133-169.
  2. Devlin, S. J.,Gnanadesikan, R.,Kettenring, J. R.(1975).Robust estimation and outlier detection with correlation coefficients.Biometrika,62,531-545.
  3. Hampel, F.(1974).The influence curve and its role in estimation.Journal of the American Statistical Association,69,383-393.
  4. Hinkley, D. V.(1977).Jackknifing in unbalanced situations.Technometrics,19,285-92.
  5. Moore, J.(1975).Dept. Agricultural Engineering, Univ. Minnesota.
  6. Peña, D.(2005).A New Statistic for Influence in Linear Regression.Technometrics,47(1),1-12.
  7. Rousseeuw, P. J.,Leroy, A. M.(1987).Robust Regression and Outlier Detection.New York:Wesley.
  8. Tukey, J. M.(1977).Exploratory Data Analysis.Addison-Wesley.
被引用次数
  1. 葉士豪(2017)。建置統計製程管制系統提升發光二極體出貨品質水準。中原大學工業與系統工程學系學位論文。2017。1-70。