Please use this identifier to cite or link to this item:
https://ah.lib.nccu.edu.tw/handle/140.119/49593| 題名: | JSWT+估計應用於線性迴歸變數選取之研究 Variable Selection Based on JSWT+ Estimator for Linear Regression |
作者: | 王政忠 Wang,Jheng-Jhong |
貢獻者: | 郭訓志 王政忠 Wang,Jheng-Jhong |
關鍵詞: | James-Stein估計量 變數選取 線性迴歸模型 minimax LASSO |
日期: | 2006 | 上傳時間: | 8-Dec-2010 | 摘要: | 變數選取方法已經成為各領域在處理多維度資料的工具。Zhou與Hwang在2005年，為了改善James-Stein positive part估計量(JS+)只能在完全模型(full model)與原始模型(origin model)兩者去做挑選，建立了具有Minimax性質同時加上門檻值的估計量，即James-Stein with Threshoding positive part估計量(JSWT+)。由於JSWT+估計量具有門檻值，使得此估計量可以在完全模型與其線性子集下做變數選取。我們想進一步了解如果將JSWT+估計量應用於線性迴歸分析時，藉由JSWT+估計具有門檻值的性質去做變數選取的效果如何？本文目的即是利用JSWT+估計量具有門檻值的性質，建立JSWT+估計量應用於線性迴歸模型變數挑選的流程。建立模擬資料分析，以可同時做係數壓縮及變數選取的LASSO方法與我們所提出JSWT+變數選取的流程去比較係數路徑及變數選取時差異比較，最後將我們提出JSWT+變數選取的流程對實際資料攝護腺癌資料(Tibshirani，1996)做變數挑選。則當考慮解釋變數個數小於樣本個數情況下，JSWT+與LASSO在變數選取的比較結果顯示，JSWT+表現的比較好，且可直接得到估計量的理想參數。 | 參考文獻: | Baranchik, A.J. (1964) Multiple regression and estimation of the mean of a multivariate normal distribution. Technical Report 51, Department of Statistics, Stanford University Stanford . Breiman, L. (1995) Better subset selection using the nonnegative garotte. Technnometrics,37,373-384 Hocking, R. R. (1976) The analysis and selection of variables in linear regression. Biometrics. 32, 1-49 Hoerl, A. E. and Kennard, R. W. (1970) Ridge regression: Biased estimation for non-orthogonal problems. Technometrics. 12,55-67 Richards, John A. (1999) An introduction James-Stein estimation Stein, C. (1956), \"Inadmissibility of the usual estimator for the mean of a multivariate distribution\", Proc. Third Berkeley Symp. Math. Statist. Prob., vol. 1, at 197-206 James, W. & C. Stein (1961), \"Estimation with quadratic loss\", Proc. Fourth Berkeley Symp. Math. Statist. Prob., vol. 1, at 311-319 Scolve,S.L.(1968).Improved estimators for voefficients in linear regression. J. Amer. Statist. Assoc. 63,597-606 Stamey, T., Kabalin, J., McNeal, J., Johnstone, I., Freiha, F., Redwine, E. and Yang, N. (1989) Prostate specific antigen in the diagnosis and treatment of adenocarcinoma of the prostate, ii: Radical prostatectomy treated patients. J. Urol., 16, 1076-1083. Stein, C. (1981) Estimation of the mean of a multivariate normal distribution. Ann. Statist., 9, 1135-1151. Tibshirani, R. (1996) Regression shrinkage and selection via the lasso. J. R. Statist. Soc. B, 58, 267–288. Zou, H. and Hastie, T (2005) Regularization and variable selection via the elastic net. J. R. Statist. Soc. B. 67, Part 2, 301–320 Zhou, H. H. and Hwang, J. T. G. (2003).Minimax estimation with thresholding. Technical report,Cornell Statistical Center. Zhou, H. H. and Hwang, J. T. G. (2005).Minimax estimation with thresholding. And its application to wavelet analysis. The Annals of Statistics. Vol. 33, No. 1, 101–125 |
描述: | 碩士 國立政治大學 統計研究所 94354022 95 |
資料來源: | http://thesis.lib.nccu.edu.tw/record/#G0094354022 | 資料類型: | thesis |
| Appears in Collections: | 學位論文 |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| 402201.pdf | 114.9 kB | Adobe PDF2 | View/Open | |
| 402202.pdf | 115.61 kB | Adobe PDF2 | View/Open | |
| 402203.pdf | 133.38 kB | Adobe PDF2 | View/Open | |
| 402204.pdf | 138.49 kB | Adobe PDF2 | View/Open | |
| 402205.pdf | 122.32 kB | Adobe PDF2 | View/Open | |
| 402206.pdf | 159.29 kB | Adobe PDF2 | View/Open | |
| 402207.pdf | 202.36 kB | Adobe PDF2 | View/Open | |
| 402208.pdf | 262.88 kB | Adobe PDF2 | View/Open | |
| 402209.pdf | 120.69 kB | Adobe PDF2 | View/Open | |
| 402210.pdf | 117.31 kB | Adobe PDF2 | View/Open | |
| 402211.pdf | 192.49 kB | Adobe PDF2 | View/Open |
Google ScholarTM
Check
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.