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Chapter 1 Robust Linear Regression: A Review and Comparison1.1 Introduction1.2 Robust Regression Methods1.2.1 M-estimates1.2.2 LMS estimates1.. LTS estimates1.2.4 S-estimates1.2.5 Generalized S-estimates (GS-estimates)1.2.6 MM-estimates1.2.7 Mallows GM-estimates1.2.8 Schweppe GM-estimates1.2.9 S1S GM-estimates1.2.10 R-estimates1.2.11 REWLSE1.2.12 Robust regression based on regularization of case-specific parameters1.3 Examples1.4 DiscussionChapter 2 A Selective Overview and Comparison of Robust Mixture Regression Estimators2.1 Introduction2.2 Robust mixture regression methods2.2.1 Robust mixture regresion using the t-distribution2.2.2 Robust mixture regression modeling using Pearson type VM distribution2.. Robust mixture regression model fitting by Laplace distribution2.2.4 Robust mixture regression modeling based on Scale mixtures of skew-normal distributions2.2.5 Robust mixture regression with random covariates via trimming and constraints2.2.6 Robust clustering in regression analysis via the contaminated gaussian cluster weighted model2.2.7 Trimmed likelihood estimator2.2.8 Least trimmed squares estimator2.2.9 Robust estimator based on a modified EM algorithm with bisquare loss2.2.10 Robust EM-type algorithm for log-concave mixtures of regression models. Simulation studies2.4 DiscussionChapter 3 Outlier Detection and Robust Mixture Modeling Using Nonconvex Penalized Likelihood3.1 Introduction3.2 Robust Mixture Model via Mean-Shift Penalization3.2.1 RMM for Equal Component Variances3.2.2 RMM for Unequal Component Variances3.. Tuning Parameter Selection3.3 Simulation3.3.1 Methods and Evaluation Measures3.3.2 Results3.4 Real Data Application3.5 DiscussionChapter 4 Outlier Detection and Robust Mixture Regression Using Nonconvex Penalized Likelihood4.1 Introduction4.2 Robust Mixture Regression via Mean-shift Penalization4.3 Simulation4.3.1 Simulation Setups4.3.2 Methods and Evaluation Measures4.3.3 Results4.4 Tone Perception Data Analysis4.5 DiscussionAppendixReferences
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