Robustness Theory and Application.

Intro -- TITLE PAGE -- COPYRIGHT PAGE -- CONTENTS -- FOREWORD -- PREFACE -- ACKNOWLEDGMENTS -- NOTATION -- ACRONYMS -- ABOUT THE COMPANION WEBSITE -- CHAPTER 1 INTRODUCTION TO ASYMPTOTIC CONVERGENCE -- 1.1 INTRODUCTION -- 1.2 PROBABILITY SPACES AND DISTRIBUTION FUNCTIONS -- 1.3 LAWS OF LARGE NUMBERS -- 1.3.1 Convergence in Probability and Almost Sure -- 1.3.2 Expectation and Variance -- 1.3.3 Statements of the Law of Large Numbers -- 1.3.4 Some History and an Example -- 1.3.5 Some More Asymptotic Theory and Application -- 1.4 THE MODUS OPERANDI RELATED BY LOCATION ESTIMATION -- 1.5 EFFICIENCY OF LOCATION ESTIMATORS -- 1.6 ESTIMATION OF LOCATION AND SCALE -- PROBLEMS -- CHAPTER 2 THE FUNCTIONAL APPROACH -- 2.1 ESTIMATION AND CONDITIONS A -- 2.2 CONSISTENCY -- 2.3 WEAK CONTINUITY AND WEAK CONVERGENCE -- 2.4 FRÉCHET DIFFERENTIABILITY -- 2.5 THE INFLUENCE FUNCTION -- 2.6 EFFICIENCY FOR MULTIVARIATE PARAMETERS -- 2.7 OTHER APPROACHES -- PROBLEMS -- CHAPTER 3 MORE RESULTS ON DIFFERENTIABILITY -- 3.1 FURTHER RESULTS ON FRÉCHET DIFFERENTIABILITY -- 3.2 M-ESTIMATORS: THEIR INTRODUCTION -- 3.2.1 Non-Smooth Analysis and Conditions A' -- 3.2.2 Existence and Uniqueness for Solutions of Equations -- 3.2.3 Results for M-estimators with Non-Smooth -- 3.3 REGRESSION M-ESTIMATORS -- 3.4 STOCHASTIC FRÉCHET EXPANSIONS AND FURTHER CONSIDERATIONS -- 3.5 LOCALLY UNIFORM FRÉCHET EXPANSION -- 3.6 CONCLUDING REMARKS -- CHAPTER 4 MULTIPLE ROOTS -- 4.1 INTRODUCTION TO MULTIPLE ROOTS -- 4.2 ASYMPTOTICS FOR MULTIPLE ROOTS -- 4.3 CONSISTENCY IN THE FACE OF MULTIPLE ROOTS -- 4.3.1 Preliminaries -- 4.3.2 Asymptotic Properties of Roots and Tests -- 4.3.3 Application of Asymptotic Theory -- 4.3.4 Normal Mixtures and Conclusion -- CHAPTER 5 DIFFERENTIABILITY AND BIAS REDUCTION -- 5.1 DIFFERENTIABILITY, BIAS REDUCTION, AND VARIANCE ESTIMATION.

5.1.1 The Jackknife Bias and Variance Estimation -- 5.1.2 Simple Location and Scale Bias Adjustments -- 5.1.3 The Bootstrap -- 5.1.4 The Choice to Jackknife or Bootstrap -- 5.2 FURTHER RESULTS ON THE NEWTON ALGORITHM -- PROBLEMS -- CHAPTER 6 MINIMUM DISTANCE ESTIMATION AND MIXTURE ESTIMATION -- 6.1 MINIMUM DISTANCE ESTIMATION AND REVISITING MIXTURE MODELING -- 6.2 THE L2-MINIMUM DISTANCE ESTIMATOR FOR MIXTURES -- 6.2.1 The L2-Estimator for Mixing Proportions -- 6.2.2 The L2-Estimator for Switching Regressions -- 6.2.3 An Example Application of Switching Regressions -- 6.3 OTHER MINIMUM DISTANCE ESTIMATION APPLICATIONS -- 6.3.1 Mixtures of Exponential Distributions -- 6.3.2 Gamma Distributions and Quality Assurance -- PROBLEMS -- CHAPTER 7 L-ESTIMATES AND TRIMMEDLIKELIHOOD ESTIMATES -- 7.1 A PREVIEW OF ESTIMATION USING ORDER STATISTICS -- 7.1.1 The Functional Form of L-Estimators of Location -- 7.2 THE TRIMMED LIKELIHOOD ESTIMATOR -- 7.2.1 LTS and Breakdown Point -- 7.2.2 TLE Asymptotics for the Normal Distribution -- 7.3 ADAPTIVE TRIMMED LIKELIHOOD AND IDENTIFICATION OF OUTLIERS -- 7.4 ADAPTIVE TRIMMED LIKELIHOOD IN REGRESSION -- 7.5 WHAT TO DO IF n IS LARGE? -- 7.5.1 TLE Asymptotics for Location and Regression -- PROBLEMS -- CHAPTER 8 TRIMMED LIKELIHOOD FOR MULTIVARIATE DATA -- 8.1 IDENTIFICATION OF MULTIVARIATE OUTLIERS -- PROBLEMS -- CHAPTER 9 FURTHER DIRECTIONS AND CONCLUSION -- 9.1 A WAY FORWARD -- PROBLEM -- APPENDIX A SPECIFIC PROOF OF THEOREM 2.1 -- APPENDIX B SPECIFIC CALCULATIONS IN EXAMPLES 4.1 AND 4.2 -- APPENDIX C CALCULATION OF MOMENTS IN EXAMPLE 4.2 -- BIBLIOGRAPHY -- INDEX -- EULA.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.