Robust Statistics

Ricardo Maronna is a Professor in the Department of Mathematics, Faculty of Exact Sciences, National University of La Plata, Argentina, and researcher at C.I.C.P.B.A. He is the author of numerous research articles on robust statistics, especially in the areas of regression and multivariate analysis.
 
Doug Martin is a Professor in the Department of Statistics, and Director of the Computational Finance Program at the University of Washington in Seattle, Washington. He was a consultant at Bell Laboratories for many years, and author of numerous research articles on robust methods for time series. Martin founded the original S-PLUS company Statistical Sciences, Inc., and led the development of the S-PLUS Robust Statistics Library.
 
Victor Yohai, is a Professor in the Department of Mathematics, Faculty of Exact and Natural Sciences, University of Buenos Aires, Argentina, and researcher at CONICET. He is the author of a large number of important research articles on robust statistics, in particular on regression and time series. Several of the procedures proposed by him have been implemented in the robust library of S-PLUS.

Classical statistical techniques fail to cope well with deviations from a standard distribution. Robust statistical methods take into account these deviations while estimating the parameters of parametric models, thus increasing the accuracy of the inference. Research into robust methods is flourishing, with new methods being developed and different applications considered.
 
Robust Statistics sets out to explain the use of robust methods and their theoretical justification. It provides an up-to-date overview of the theory and practical application of the robust statistical methods in regression, multivariate analysis, generalized linear models and time series. This unique book:
* Enables the reader to select and use the most appropriate robust method for their particular statistical model.
* Features computational algorithms for the core methods.
* Covers regression methods for data mining applications.
* Includes examples with real data and applications using the S-Plus robust statistics library.
* Describes the theoretical and operational aspects of robust methods separately, so the reader can choose to focus on one or the other.
* Supported by a supplementary website featuring time-limited S-Plus download, along with datasets and S-Plus code to allow the reader to reproduce the examples given in the book.
 
Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is ideal for researchers, practitioners and graduate students of statistics, electrical, chemical and biochemical engineering, and computer vision. There is also much to benefit researchers from other sciences, such as biotechnology, who need to use robust statistical methods in their work.

Robust Statistics fills the need for a solid, up to date text that presents a broad overview of the theory of robust statistics, integrated with applications and computing. The book features in depth coverage of the key methodology, including regression, multivariate analysis, and time series.

Preface.
 
INTRODUCTION.
 
Classical and robust approaches to statistics.
 
Mean and standard deviation.
 
The "three-sigma edit" rule.
 
Linear regression.
 
Correlation coefficients.
 
Other parametric models.
 
Problems.
 
LOCATION AND SCALE.
 
The location model.
 
M-estimates of location.
 
Trimmed means.
 
Dispersion estimates.
 
M-estimates of scale.
 
M-estimates of location with unknown dispersion.
 
Numerical computation of M-estimates.
 
Robust confidence intervals and tests.
 
Appendix: proofs and complements.
 
Problems.
 
MEASURING ROBUSTNESS.
 
The influence function.
 
The breakdown point.
 
Maximum asymptotic bias.
 
Balancing robustness and efficiency.
 
*"Optimal" robustness.
 
Multidimensional parameters.
 
*Estimates as functionals.
 
Appendix: proofs of results.
 
Problems.
 
LINEAR REGRESSION 1.
 
Introduction.
 
Review of the LS method.
 
Classical methods for outlier detection.
 
Regression M-estimates.
 
Numerical computation of monotone M-estimates.
 
Breakdown point of monotone regression estimates.
 
Robust tests for linear hypothesis.
 
*Regression quantiles.
 
Appendix: proofs and complements.
 
Problems.
 
LINEAR REGRESSION 2.
 
Introduction.
 
The linear model with random predictors 118
 
M-estimates with a bounded Á-function.
 
Properties of M-estimates with a bounded Á-function.
 
MM-estimates.
 
Estimates based on a robust residual scale.
 
Numerical computation of estimates based on robust scales.
 
Robust confidence intervals and tests for M-estimates.
 
Balancing robustness and efficiency.
 
The exact fit property.
 
Generalized M-estimates.
 
Selection of variables.
 
Heteroskedastic errors.
 
*Other estimates.
 
Models with numeric and categorical predictors.
 
*Appendix: proofs and complements.
 
Problems.
 
MULTIVARIATE ANALYSIS.
 
Introduction.
 
Breakdown and efficiency of multivariate estimates.
 
M-estimates.
 
Estimates based on a robust scale.
 
The Stahel-Donoho estimate.
 
Asymptotic bias.
 
Numerical computation of multivariate estimates.
 
Comparing estimates.
 
Faster robust dispersion matrix estimates.
 
Robust principal components.
 
*Other estimates of location and dispersion.
 
Appendix: proofs and complements.
 
Problems.
 
GENERALIZED LINEAR MODELS.
 
Logistic regression.
 
Robust estimates for the logistic model.
 
Generalized linear models.
 
Problems.
 
TIME SERIES.
 
Time series outliers and their impact.
 
Classical estimates for AR models.
 
Classical estimates for ARMA models.
 
M-estimates of ARMA models.
 
Generalized M-estimates.
 
Robust AR estimation using robust filters.
 
Robust model identification.
 
Robust ARMA model estimation using robust filters.
 
ARIMA and SARIMA models.
 
Detecting time series outliers and level shifts.
 
Robustness measures for time series.
 
Other approaches for ARMA models.
 
High-efficiency robust location estimates.
 
Robust spectral density estimation.
 
Appendix A: heuristic derivation of the asymptotic distribution of

Lieferung vom Verlag mit leichten Qualitätsmängeln möglich