Return to Coronet Books main page

Robustness in Data Analysis: Criteria and MethodsBy Georgy L. Shevlyakov and Nikita O. Vilchevski

December 2001

VSP

ISBN: 90-6764-351-3

324 pages

$187.50 hardcover

The field of mathematical statistics called robustness statistics deals with the stability of statistical inference under variations of accepted distribution models. Although robust statistics involves mathematically highly defined tools, robust methods exhibit a satisfactory behaviour in small samples, thus being quite useful in applications.This volume in the book series Modern Probability and Statistics addresses various topics in the field of robust statistics and data analysis, such as: a probability-free approach in data analysis; minimax variance estimators of location, scale, regression, autoregression and correlation; L1-norm methods; adaptive, data reduction, bivariate boxplot, and multivariate outlier detection algorithms; applications in reliability, detection of signals, and analysis of the sudden cardiac death risk factors.

The book contains new results related to robustness and data analysis technologies, including both theoretical aspects and practical needs of data processing, which have been relatively inaccessible as they were originally only published in Russian.

This book will be of value and interest to researchers in mathematical statistics as well as to those using statistical methods.

Contents:

- INTRODUCTION
- General remarks
- Huber minimax approach
- Hampel approach
- OPTIMIZATION CRITERIA IN DATA ANALYSIS: A PROBABILITY-FREE APPROACH
- Introductory remarks
- Translation and scale equivariant contrast functions
- Orthogonal equivariant contrast functions
- Monotonically equivariant contrast functions
- Minimal sensitivity to small perturbations in the data
- Affine equivariate contrast functions
- ROBUST MIMIMAX ESTIMATION OF LOCATION
- Introductory remarks
- Robust estimation of location in models with bounded variances
- Robust estimation of location in models with bounded subranges
- Robust estimators of multivariate location
- Least informative lattice distributions
- ROBUST ESTIMATION OF SCALE
- Introductory remarks; Measures of scale defined by functionals
M-, L-,andR-estimators of scale- Huber minimax estimator of scale
- Final remarks
- ROBUST REGRESSION AND AUTOREGRESSION
- Introductory remarks
- The minimax variance regression
- Robust autoregression
- Robust identification in dynamic models
- Final remarks
- ROBUSTNESS OF
L_{1}-NORM ESTIMATORS- Introductory remarks
- Stability of
L_{1}-approximations- Robustness of the
L_{1}-regression- Final remarks
- ROBUST ESTIMATION OF CORRELATION
- Introductory remarks
- Analysis: Monte Carlo experiment
- Analysis: asymptotic characteristics
- Synthesis: minimax variance correlation
- Two-stage estimators: rejection of outliers plus classics
- COMPUTATION AND DATA ANALYSIS TECHNOLOGIES
- Introductory remarks on computation
- Adaptive robust procedures
- Smoothing quantile functions by the Bernstein polynomials
- Robust bivariate boxplots
- APPLICATIONS
- On robust elimination in the statistical theory of reliability
- Robust detection of signals based on optimisation criteria
- Statistical analysis of sudden cardiac death risk factors
BibliographyIndexMathematics

Modern Probability & Statistics Series