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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/86786


    Title: 有影響力自變數的偵測
    Authors: 盧惟真
    Contributors: 宋傳欽
    盧惟真
    Keywords: 有影響力自變數
    Kullback-Leibler對稱散度
    貝氏方法
    廣義變異膨脹矩陣
    共線性
    Date: 1998
    Issue Date: 2016-04-27 16:43:17 (UTC+8)
    Abstract: 在一個具有多個自變數的線性模式中，當我們發現模式在加入或刪除某些自變數時，若對其他參數的估計或估計分配或後驗分配造成極大的影響，我們就有必要提出警告訊息並做進一步分析。而偵測這些造成影響之自變數的方法，除了Schall和Dunne（1990）所提的Cook距離和AP統計量外，本文提出用Kullback-Leibler對稱散度的方法，以自變數增加前後，參數估計分配間的差異作為所加入之自變數影響力的指標。另一方面，就貝氏的觀點，以自變數增加前後，參數後驗分配間的差異程度作為偵測有影響力自變數的方法。此外，本文亦探索Kullback-Leibler對稱散度與自變數間共線性的關係。
    Reference: [1] Box, G. E. P. and Tiao, G. C. (1973), Bayesian Inference in Statistical Analysis, Addison-Wesley Publishing Co.
    [2] Chaloner K. and Brant R. (1988), "A Bayesian approach to outlier detection and residual analysis," Biometrika , 75, 4, 651-659.
    [3] Draper, N. R. and John, J. A. (1981), "Influential Observations and Outliers in Regression," Technometrics, 23, 21-26.
    [4] Fox, J. and Monette, G. (1992), "Generalized Collinearity Diagnostics," Journal of American Statistical Association, 87, 178-183.
    [5] Guttman, I. and Pena, D. (1988), Outliers and Influence: Evaluation by posteriors of parameters in the linear model, Bayesian Statistics 3, 631-640.
    [6] Rao, C. R. (1973), Linear Statistical Inference and Its Applications, 2nd edition, John Wiley, New York.
    [7] Schall, R. and Dunne, T. T. (1990), "Influential Variables in Linear Regression," Technometrics, 32, 323-330.
    [8] Seber, G. A. F. (1977), Linear Regression Analysis, John Wiley, New York.
    [9] Weisberg, S. (1980), Applied Linear Regression, John Wiley, New York.
    Description: 碩士
    國立政治大學
    應用數學系
    86751001
    Source URI: http://thesis.lib.nccu.edu.tw/record/#B2002001692
    Data Type: thesis
    Appears in Collections:[Department of Mathematical Sciences] Theses

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