Robust statistics : theory and methods (with R)

Robust statistics : theory and methods (with R) / Ricardo A. Maronna [and 3 others]

A new edition of this popular text on robust statistics, thoroughly updated to include new and improved methods and focus on implementation of methodology using the increasingly popular open-source software R. Classical statistics fail to cope well with outliers associated with deviations from stand...

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Bibliographic Details
Main Author: Maronna, Ricardo A. (Author)
Format: eBook
Language:English
Published: [Place of publication not identified] : Wiley, [2018]
Edition:Second edition.
Subjects:
Robust statistics.
MATHEMATICS > Applied.
MATHEMATICS > Probability & Statistics > General.
Robust statistics
Online Access:Click for online access
Table of Contents:
  • Cover; Title Page; Copyright; Contents; Preface; Preface to the First Edition; About the Companion Website; Chapter 1 Introduction; 1.1 Classical and robust approaches to statistics; 1.2 Mean and standard deviation; 1.3 The "three sigma edit" rule; 1.4 Linear regression; 1.4.1 Straight-line regression; 1.4.2 Multiple linear regression; 1.5 Correlation coefficients; 1.6 Other parametric models; 1.7 Problems; Chapter 2 Location and Scale; 2.1 The location model; 2.2 Formalizing departures from normality; 2.3 M-estimators of location; 2.3.1 Generalizing maximum likelihood
  • 2.3.2 The distribution of M-estimators2.3.3 An intuitive view of M-estimators; 2.3.4 Redescending M-estimators; 2.4 Trimmed and Winsorized means; 2.5 M-estimators of scale; 2.6 Dispersion estimators; 2.7 M-estimators of location with unknown dispersion; 2.7.1 Previous estimation of dispersion; 2.7.2 Simultaneous M-estimators of location and dispersion; 2.8 Numerical computing of M-estimators; 2.8.1 Location with previously-computed dispersion estimation; 2.8.2 Scale estimators; 2.8.3 Simultaneous estimation of location and dispersion; 2.9 Robust confidence intervals and tests
  • 2.9.1 Confidence intervals2.9.2 Tests; 2.10 Appendix: proofs and complements; 2.10.1 Mixtures; 2.10.2 Asymptotic normality of M-estimators; 2.10.3 Slutsky's lemma; 2.10.4 Quantiles; 2.10.5 Alternative algorithms for M-estimators; 2.11 Recommendations and software; 2.12 Problems; Chapter 3 Measuring Robustness; 3.1 The influence function; 3.1.1 *The convergence of the SC to the IF; 3.2 The breakdown point; 3.2.1 Location M-estimators; 3.2.2 Scale and dispersion estimators; 3.2.3 Location with previously-computed dispersion estimator; 3.2.4 Simultaneous estimation
  • 3.2.5 Finite-sample breakdown point3.3 Maximum asymptotic bias; 3.4 Balancing robustness and efficiency; 3.5 *"Optimal" robustness; 3.5.1 Bias- and variance-optimality of location estimators; 3.5.2 Bias optimality of scale and dispersion estimators; 3.5.3 The infinitesimal approach; 3.5.4 The Hampel approach; 3.5.5 Balancing bias and variance: the general problem; 3.6 Multidimensional parameters; 3.7 *Estimators as functionals; 3.8 Appendix: Proofs of results; 3.8.1 IF of general M-estimators; 3.8.2 Maximum BP of location estimators; 3.8.3 BP of location M-estimators

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