Robustness in Data Analysis: Criteria and Methods

✍ Scribed by Georgy L. Shevlyakov; Nikita O. Vilchevski

• Publisher: De Gruyter
• Year: 2011
• Tongue: English
• Leaves: 324
• Category: Library

✦ Table of Contents

Foreword
Preface
1 Introduction
1.1 General remarks
1.2 Huber minimax approach
1.3 Hampel approach
2 Optimization criteria in data analysis: a probability-free approach
2.1 Introductory remarks
2.2 Translation and scale equivariant contrast functions
2.3 Orthogonal equivariant contrast functions
2.4 Monotonically equivariant contrast functions
2.5 Minimal sensitivity to small perturbations in the data
2.6 Affine equivariant contrast functions
3 Robust minimax estimation of location
3.1 Introductory remarks
3.2 Robust estimation of location in models with bounded variances
3.3 Robust estimation of location in models with bounded subranges
3.4 Robust estimators of multivariate location
3.5 Least informative lattice distributions
4 Robust estimation of scale
4.1 Introductory remarks
4.2 Measures of scale defined by functionals
4.3 M-, L-, and R-estimators of scale
4.4 Huber minimax estimator of scale
4.5 Final remarks
5 Robust regression and autoregression
5.1 Introductory remarks
5.2 The minimax variance regression
5.3 Robust autoregression
5.4 Robust identification in dynamic models
5.5 Final remarks
6 Robustness of L1-norm estimators
6.1 Introductory remarks
6.2 Stability of L1-approximations
6.3 Robustness of the L1-regression
6.4 Final remarks
7 Robust estimation of correlation
7.1 Introductory remarks
7.2 Analysis: Monte Carlo experiment
7.3 Analysis: asymptotic characteristics
7.4 Synthesis: minimax variance correlation
7.5 Two-stage estimators: rejection of outliers plus classics
8 Computation and data analysis technologies
8.1 Introductory remarks on computation
8.2 Adaptive robust procedures
8.3 Smoothing quantile functions by the Bernstein polynomials
8.4 Robust bivariate boxplots
9 Applications
9.1 On robust estimation in the statistical theory of reliability
9.2 Robust detection of signals based on optimization criteria
9.3 Statistical analysis of sudden cardiac death risk factors
Bibliography
Index