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研究生:黃信雄
研究生(外文):Hsin-Hsiung Huang
論文名稱:使用Lasso-Cp選取線性模型解釋變數之探討
論文名稱(外文):Study on the Lasso Method for Variable Selectionin Linear Regression Model with Mallows'' Cp
指導教授:陳宏陳宏引用關係
指導教授(外文):Hung Chen
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2006
畢業學年度:95
語文別:英文
論文頁數:46
中文關鍵詞:最小角度回歸
外文關鍵詞:Least angle regressionForward selection
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當線性回歸模型中的自變數極多時, 正規化是個常用的辦法來達到降低被選取回歸模型複雜度之目的。Lasso (Tibshirani, 1996) 被認為是可以達到選取模型參數精簡目的之正規化方法。當線性回歸模型中的自變數為么正且自變數個數及樣本數個數相近時, 本論文探討使用Lasso 與Cp辦法選擇重要自變數的操作性質。考慮的操作性質, 包含了被選取自變數的個數及被選取真實自變數佔被選取自變數的比例。當Lasso 與Cp作為多重假設檢定辦法時, 這些結論也適用之。
When the number of predictors in a linear regression model is large, regularization is a commonly used method to reduce the complexity of the fitted model. LASSO (Tibshirani, 1996) is being advocated as a useful regulation
method for achieving sparsity or parsimony of resulting fitted model. In this thesis, we study the operating characteristics of LASSO coupled with Mallows’Cp on identifying the orthonormal predictor variables of linear regression when the number of predictors and the number of the observation are of the same magnitude. The characteristics includes the chosen number of predictors and the proportion of correctly identified predictors. This result can be useful in multiple testing.
目錄
口試委員會審定書.......................................i
誌謝...................................................ii
中文摘要...............................................iii
英文摘要...............................................iv
第一章Introduction.....................................1
第二章Lasso............................................3
第一節Multiple Hypothesis Testing......................4
第二節Regression.......................................9
第三章Random walk induced by Mallows''Cp................11
第四章Estimate of the degrees of freedom...............16
第五章Null and Sparse Models...........................23
第六章Simulation Studies When n = m and Xnm = Im.......25
第一節Study 1: Null Model..............................26
第二節Study 2: The spacings determined by 2exp(1)-2....27
第三節Study 3: Sparse Model with Cp of Penalty 2.......28
第四節Study 4: Sparse Model with Cp of Penalty 4.......31
第五節Study 5: Effect on Penalty 4 and 2 under Abundant
Models.................................................33
第七章Simulation Studies When n~5m and XTnmXnm=Im......36
第一節Study 6: Null Model..............................36
第二節Study 7: Effect on Penalty 4 and 2 under Sparse Model..................................................37
第三節Study 8: Effect on Penalty 4 and 2 under Abundant
Models.................................................39
第八章Conclusions and Discussions......................41
參考文獻...............................................44
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