穩健混合模型（簡體書）

《穩健混合模型》提出了經由均值漂移懲罰的穩健混合模型方法(RMM)和穩健混合回歸模型方法(RM2)，這兩種方法可以同時進行參數估計和離群值檢測。一個均值漂移參數γ，被引入到混合模型(混合回歸模型)中，並用非凸的懲罰函數對其加以懲罰。這些非凸的懲罰函數都有對應的鬧值法則用於對該均值漂移參數的估計。基於這樣的模型設定，我們提出了一種選代的間值嵌入式的EM算法對懲罰目標函數大化進行參數估計。通過和其他的穩健混合回歸模型方法進行比較，我們提出的RMM和RM2方法在離群值檢測和參數估計兩個方面都有更優的表現。

余純，統計學博士，現任江西財經大學統計學院副教授。研究方向為穩健線性回歸、穩健混合模型、變量與模型選擇以及精算科學等。主要講授“金融數學”“精算概率”“概率論”“線性模型方法”以及“數理統計前沿問題研究”等大學本科和研究生課程。

Chapter 1 Robust Linear Regression： A Review and Comparison
1．1 Introduction
1．2 Robust Regression Methods
1．2．1 M-estimates
1．2．2 LMS estimates
1．2．3 LTS estimates
1．2．4 S-estimates
1．2．5 Generalized S-estimates (GS-estimates)
1．2．6 MM-estimates
1．2．7 Mallows GM-estimates
1．2．8 Schweppe GM-estimates
1．2．9 S1S GM-estimates
1．2．10 R-estimates
1．2．11 REWLSE
1．2．12 Robust regression based on regularization of case-specific parameters
1．3 Examples
1．4 Discussion

Chapter 2 A Selective Overview and Comparison of Robust Mixture Regression Estimators
2．1 Introduction
2．2 Robust mixture regression methods
2．2．1 Robust mixture regresion using the t-distribution
2．2．2 Robust mixture regression modeling using Pearson type VM distribution
2．2．3 Robust mixture regression model fitting by Laplace distribution
2．2．4 Robust mixture regression modeling based on Scale mixtures of skew-normal distributions
2．2．5 Robust mixture regression with random covariates via trimming and constraints
2．2．6 Robust clustering in regression analysis via the contaminated gaussian cluster weighted model
2．2．7 Trimmed likelihood estimator
2．2．8 Least trimmed squares estimator
2．2．9 Robust estimator based on a modified EM algorithm with bisquare loss
2．2．10 Robust EM-type algorithm for log-concave mixtures of regression models
2．3 Simulation studies
2．4 Discussion

Chapter 3 Outlier Detection and Robust Mixture Modeling Using Nonconvex Penalized Likelihood
3．1 Introduction
3．2 Robust Mixture Model via Mean-Shift Penalization
3．2．1 RMM for Equal Component Variances
3．2．2 RMM for Unequal Component Variances
3．2．3 Tuning Parameter Selection
3．3 Simulation
3．3．1 Methods and Evaluation Measures
3．3．2 Results
3．4 Real Data Application
3．5 Discussion

Chapter 4 Outlier Detection and Robust Mixture Regression Using Nonconvex Penalized Likelihood
4．1 Introduction
4．2 Robust Mixture Regression via Mean-shift Penalization
4．3 Simulation
4．3．1 Simulation Setups
4．3．2 Methods and Evaluation Measures
4．3．3 Results
4．4 Tone Perception Data Analysis
4．5 Discussion
Appendix
References