Robustness theory and application. (2018)

• Record Type: Book
• Further Information: Note: Brenton R. Clarke.
• Authors: Clarke, Brenton R
• Contents: Foreword xi Preface xv Acknowledgments xvii Notation xix Acronyms xxi About the Companion Website xxiii 1 Introduction to Asymptotic Convergence 1 1.1 Introduction, 1 1.2 Probability Spaces and Distribution Functions, 2 1.3 Laws of Large Numbers, 3 1.3.1 Convergence in Probability and Almost Sure, 3 1.3.2 Expectation and Variance, 4 1.3.3 Statements of the Law of Large Numbers, 4 1.3.4 Some History and an Example, 5 1.3.5 Some More Asymptotic Theory and Application, 6 1.4 The Modus Operandi Related by Location Estimation, 8 1.5 Efficiency of Location Estimators, 17 1.6 Estimation of Location and Scale, 20 2 The Functional Approach 27 2.1 Estimation and Conditions A, 27 2.2 Consistency, 37 2.3 Weak Continuity and Weak Convergence, 41 2.4 Fréchet Differentiability, 44 2.5 The Influence Function, 48 2.6 Efficiency for Multivariate Parameters, 51 2.7 Other Approaches, 52 3 More Results on Differentiability 59 3.1 Further Results on Fréchet Differentiability, 59 3.2 M-Estimators: Their Introduction, 59 3.2.1 Non-Smooth Analysis and Conditions A′, 61 3.2.2 Existence and Uniqueness for Solutions of Equations, 65 3.2.3 Results for M-estimators with Non-Smooth Ψ, 67 3.3 Regression M-Estimators, 70 3.4 Stochastic Fréchet Expansions and Further Considerations, 73 3.5 Locally Uniform Fréchet Expansion, 74 3.6 Concluding Remarks, 76 4 Multiple Roots 79 4.1 Introduction to Multiple Roots, 79 4.2 Asymptotics for Multiple Roots, 80 4.3 Consistency in the Face of Multiple Roots, 82 4.3.1 Preliminaries, 83 4.3.2 Asymptotic Properties of Roots and Tests, 92 4.3.3 Application of Asymptotic Theory, 94 4.3.4 Normal Mixtures and Conclusion, 97 5 Differentiability and Bias Reduction 99 5.1 Differentiability, Bias Reduction, and Variance Estimation, 99 5.1.1 The Jackknife Bias and Variance Estimation, 99 5.1.2 Simple Location and Scale Bias Adjustments, 102 5.1.3 The Bootstrap, 105 5.1.4 The Choice to Jackknife or Bootstrap, 107 5.2 Further Results on the Newton Algorithm, 108 6 Minimum Distance Estimation and Mixture Estimation 113 6.1 Minimum Distance Estimation and Revisiting Mixture Modeling, 113 6.2 The L2-Minimum Distance Estimator for Mixtures, 125 6.2.1 The L2-Estimator for Mixing Proportions, 126 6.2.2 The L2-Estimator for Switching Regressions, 130 6.2.3 An Example Application of Switching Regressions, 133 6.3 Other Minimum Distance Estimation Applications, 135 6.3.1 Mixtures of Exponential Distributions, 136 6.3.2 Gamma Distributions and Quality Assurance, 139 7 L-Estimates and Trimmed Likelihood Estimates 147 7.1 A Preview of Estimation Using Order Statistics, 147 7.1.1 The Functional Form of L-Estimators of Location, 150 7.2 The Trimmed Likelihood Estimator, 152 7.2.1 LTS and Breakdown Point, 154 7.2.2 TLE Asymptotics for the Normal Distribution, 156 7.3 Adaptive Trimmed Likelihood and Identification of Outliers, 160 7.4 Adaptive Trimmed Likelihood in Regression, 163 7.5 What to do if n is Large?, 169 7.5.1 TLE Asymptotics for Location and Regression, 170 8 Trimmed Likelihood for Multivariate Data 175 8.1 Identification of Multivariate Outliers, 175 9 Further Directions and Conclusion 181 9.1 A Way Forward, 181 Appendix A Specific Proof of Theorem 2.1 187 Appendix B Specific Calculations in Examples 4.1 and 4.2 189 Appendix C Calculation of Moments in Example 4.2 193 Bibliography 195 Index 211
• Edition: 1st
• Publisher Details: Hoboken, New Jersey : John Wiley & Sons, Inc
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 519.5; Robust statistics
• Languages: English
• ISBNs: 9781118669372; 9781118669501; 9781118669464
• Related ISBNs: 9781118669303
• Notes: Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.