Polyteknisk Boghandel

Robust Statistics, Second Edition includes four new chapters on the following topics: robust tests; small sample asymptotics; breakdown point; and Bayesian robustness. A new section on time series has also been included. The first edition of this book was the first systematic, book-length treatment of robust statistics. The book begins with a general introduction and the formal mathematical background behind qualitative and quantitative robustness. A solid foundation of robust statistics for both the theoretical and the applied statistician is provided. The book successfully reorganizes, summarizes, and extends information that has been available in part thus far. Concepts are stressed throughout rather than mathematical completeness, and selected numerical algorithms for computing robust estimates, as well as convergence proofs, are provided. Quantitative robustness information for a variety of estimates is contained within tables throughout.

Preface
Preface
to First Edition.
1. Generalities.
1.
1 Why Robust Procedures?1.
2 What Should a Robust Procedure Achieve?1.
3 Qualitative Robustness.
1.
4 Quantitative Robustness.
1.
5 Infinitesimal Aspects.
1.
6 Optimal Robustness.
1.
7 Computation of Robust Estimates.
1.
8 Limitations to Robustness Theory.
2. The Weak Topology and its Metrization.
2.
1 General Remarks.
2.
2 The Weak Topology.
2.
3 L_vy and Prohorov Metrics.
2.
4 The Bounded Lipschitz Metric.
2.
5 Fr_echet and G'teaux Derivatives.
2.
6 Hampel's Theorem.
3. The Basic Types of Estimates.
3.
1 General Remarks.
3.
2 Maximum Likelihood Type Estimates (MEstimates).
3.
3 Linear Combinations of Order Statistics (LEstimates).
3.
4 Estimates Derived from Rank Tests (REstimates).
3.
5 Asymptotically Efficient M, L, and REstimates.
4. Asymptotic Minimax Theory for Estimating Location.
4.
1 General Remarks.
4.
2 Minimax Bias.
4.
3 Minimax Variance: Preliminaries.
4.
4 Distributions Minimizing Fisher Information.
4.
5 Determination of F0 by Variational Methods.
4.
6 Asymptotically Minimax MEstimates.
4.
7 On the Minimax Property for Land REstimates.
4.
8 Redescending MEstimates.
4.
9 Questions of Asymmetric Contamination.
5. Scale Estimates.
5.
1 General Remarks.
5.
2 MEstimates of Scale.
5.
3 LEstimates of Scale.
5.
4 REstimates of Scale.
5.
5 Asymptotically Efficient Scale Estimates.
5.
6 Distributions Minimizing Fisher Information for Scale.
5.
7 Minimax Properties.
6. Multiparameter Problems, in Particular Joint Estimation of Location and Scale.
6.
1 General Remarks.
6.
2 Consistency of MEstimates.
6.
3 Asymptotic Normality of MEstimates.
6.
4 Simultaneous MEstimates of Location and Scale.
6.
5 MEstimates with Preliminary Estimates of Scale.
6.
6 Quantitative Robustness of Joint Estimates of Location and Scale.
6.
7 The Computation of MEstimates of Scale.
6.
8 Studentizing.
7. Regression.
7.
1 General Remarks.
7.
2 The Classical Linear Least Squares Case.
7.
2.
1 Residuals and Outliers.
7.
3 Robustizing the Least Squares Approach.
7.
4 Asymptotics of Robust Regression Estimates.
7.
5 Conjectures and Empirical Results.
7.
6 Asymptotic Covariances and Their Estimation.
7.
7 Concomitant Scale Estimates.
7.
8 Computation of Regression MEstimates.
7.
9 The Fixed Carrier Case: what size hi?7.
10 Analysis of Variance.
7.
11 L1estimates and Median Polish.
7.
12 Other Approaches to Robust Regression.
8. Robust Covariance and Correlation Matrices.
8.
1 General Remarks.
8.
2 Estimation of Matrix Elements Through Robust Variances.
8.
3 Estimation of Matrix Elements Through Robust Correlation.
8.
4 An Affinely Equivariant Approach.
8.
5 Estimates Determined by Implicit Equations.
8.
6 Existence and Uniqueness of Solutions.
8.
7 Influence Functions and Qualitative Robustness.
8.
8 Consistency and Asymptotic Normality.
8.
9 Breakdown Point.
8.
10 Least Informative Distributions.
8.
11 Some Notes on Computation.
9. Robustness of Design.
9.
1 General Remarks.
9.
2 Minimax Global Fit.
9.
3 Minimax Slope.
10. Exact Finite S