淡江大學覺生紀念圖書館 (TKU Library)
進階搜尋


下載電子全文限經由淡江IP使用) 
系統識別號 U0002-1306200623584300
中文論文名稱 分數檢定在迴歸上的應用
英文論文名稱 Use The Score Test In Regression
校院名稱 淡江大學
系所名稱(中) 數學學系碩士班
系所名稱(英) Department of Mathematics
學年度 94
學期 2
出版年 95
研究生中文姓名 張元駿
研究生英文姓名 Yuan-Chun Chang
學號 693150061
學位類別 碩士
語文別 英文
口試日期 2006-05-19
論文頁數 33頁
口試委員 指導教授-王國徵
委員-吳錦全
委員-林秋華
中文關鍵字 分數檢定 
英文關鍵字 Score test 
學科別分類 學科別自然科學數學
中文摘要 在迴歸分析的使用上,我們必須要檢測所設定迴歸模型符合迴歸的三個基本假設,分別為(1)獨立假設、(2)常態假設、(3)常數變異數。而針對每個假設,很多學者也分別提出了一些檢定的方法。

在1983年,R. Dennis Cook & Sanford Weisberg 對於常數變異數這個假設提出了一個檢定方法。他們利用分數檢定來檢定模型是否符合此假設,並用圖形來加以輔助,不過並未加以證明。

在此篇論文中,我們嘗試證明他們在當時所做出來的結果,並提供SAS的程式。
英文摘要 In using Regression model, we have to support these three basic assumptions which in Regression. They are (1) Independence, (2) Normality, and (3) Constant Variance. And many scholars provide several diagnostic techniques for each assumption.

In 1983, R. Dennis Cook & Sanford Weisberg were given a diagnostic method for checking the assumption of constant variance. They try to use the score test to test if the model satisfies the assumption or not. And use the graphic to complement the score test.But without prove all of the result.

In this dissertation, we try to prove the result that they did in 1983.
論文目次 1. Introduction.......................................1
2. Tests concerning nonconstant variance..............1
2.1. Models..........................................1
2.2 Score tests......................................3
2.2..1 Notations....................................3
2.2..2 Find MLE of β and σ.........................4
2.2..3 Information matrix...........................4
2.2..4 The score test statistic.....................7
2.2..5 The distribution of score test statistic.....9
3. Graphical Methods.................................14
4. Illustrations.....................................17
4.1 Cherry trees....................................17
4.2 Gas vapours.....................................18
5. Comments..........................................21
6. References........................................23
7. Appendix..........................................25
7.1 SAS program for test statistics.................25
7.2 SAS program for graphical methods...............29
List of Tables
1 Simulated percentage points from the small-sample null distribution of the score statistic..................13
2 Score tests (a) tree data; (b) gas vapour data.....20
List of Figures
1 ei versus fitted values; tree data..................20
2 ri^2 versus (1-vii)H; tree data.......................20
3 ri versus fitted values; gas vapour data............20
4 ri^2 versus (1-vii)yi; gas vapour data.................20
5 ri^2 versus (1-vii)X1; gas vapour data................21
6 ri^2 versus (1-vii)gi, where the gi are the fitted values from the regression of ei^2/σ^2 on X1 and X4; gas vapour data.....21
參考文獻 ANSCOMBE, F. (1961). Examination of residuals. Proc. 4th Berkeley symp. 1, 1-36.

ATKINSON, A. C. (1973). Testing transformations to normality. J. R. Statist. Soc. B35, 473-9.

ATKINSON, A. C. (1981). Two graphical displays for outlying and influential observations in regression. Biometrika 68, 13-20.

ATKINSON, A. C. (1982). Regression diagnostics, transformations and constructed variables (with discussion). J. R. Statist. Soc. B 44, 1-35.

BICKEL, P. (1978). Using residuals robustly I: Tsets for heteroscedasticity, nonlinearity. Ann. Statist. 6, 266-91.

BICKEL, P. J. & DOKSUM, K. A. (2001). Mathematical statistics-Basic ideas and selected topics vol. I. 2nd ed, 398-400.

BOX, G. E. P. (1980). Sampling and Bayes' inference in scientific modelling and robustness (with discussion). J. R. Statist. Soc. A 143, 383-430.

BOX, G. E. P. & HILL, W. J. (1974). Correcting inhomogeneity of variances with power transformation weighting. Technometrics 16, 385-9.

CARROLL, R. J. & RUPPERT, D. (1981). On robust tests for heteroscedasticity. Ann. Statist. 9, 205-9.

COOK, R. D. & WEISBERG, S. (1980). Characterizations of an empirical influence function for detecting influential cases in regression. Technometrics 22, 495-508.

COOK, R. D. & WEISBERG, S. (1982). Residuals and Influence in Regression. London: Chapman & Hall.

COOK, R. D. & WEISBERG, S. (1983). Diagnostics for heteroscedasticity in regression.

COOK, R. D. & WEISBERG, S. (1994). An introduction to regression graphics, 182-189.

COX, D. R. & HINKLKEY, D. V. (1974). Theoretical Statistics. London: Chapman & Hall.

DURBIN, J. & WATSON, G. S. (1971). Testing for serial correlation in least squares regression, III. Biometrika 58, 1-19.

GLEJSER, H. (1969). A new test for heteroscedasticity. J. Am. Statist. Assoc. 64, 316-23.

GOLDFELD, S. M. & QUANDT, R. E. (1965). Some tests for heteroscedasticity. J. Am. Statist. Assoc. 60, 539-47.

HAMMERSTROM, T. (1981). Asymptotically optimal tests for heteroscedasticity in the general linear model. Ann. Statist. 9, 368-80.

HARRISON, M. J. & MCCABE, B. P. M. (1979). A test for heteroscedasticity based on ordinary least squares residuals. J. Am. Statistic. Assoc. 74, 494-500

HORN, P. (1981). Heteroscedasticity of residuals: A non-parametric alternative to the Goldfeld-Quandt peak test. Comm. Statist. A 10, 795-808.

JOBSON, J. D. & FULLER, W. A. (1980). Least squares estimation when the covariance matrix and parameter vector are functionally related. J. Am. Statist. Assoc. 75, 176-81.

MARSAGLIA, G. & BRAY, T. A. (1964). A convenient method for generating normal variables. S.I.A.M. Rev. 6, 260-4.

NELDER, J. A. & WEDDERBURN, R. W. M. (1972). Generalized linear models. J. A. Statist. Soc. A35, 370-84.

PREGIBON, D. (1981). Logistic regression diagnostics. Ann. Statist. 9, 705-24.

Ryan, T., Joiner, B. & Ryan, B. (1976). Minitab student handbook. North Scituate, Mass: Duxbury.

Weisberg, S. (1980). Applied linear regression. New York: Wiley.
論文使用權限
  • 同意紙本無償授權給館內讀者為學術之目的重製使用,於2006-06-20公開。
  • 同意授權瀏覽/列印電子全文服務,於2006-06-20起公開。


  • 若您有任何疑問,請與我們聯絡!
    圖書館: 請來電 (02)2621-5656 轉 2281 或 來信