Robust Statistics Through the Monitoring Approach
Description
This open access book presents robust statistical methods and procedures through the monitoring approach, with an emphasis on applications to linear regression. Illustrating the theory, it explores both large and small-sample properties. The performance of the forward search and of the monitoring of static robust estimators for regression data are illuminated through numerous data analyses using MATLAB and R.
The book describes the results of many years' work of the authors in the development of powerful methods of robust regression analysis. Robust methods are designed to analyse contaminated data. The well-established static robust methods estimate model features, such as parameter estimates, assuming the amount of contamination in the data is known. These methods are described in detail in Chapter 2 for estimation in a simple sample. The extension to regression is presented in Chapter 3, with an emphasis on S-estimation and related procedures as well as on least trimmed squares. The monitoring methods of Chapter 4, including the forward search, find the appropriate level of robustness for each data set and so avoid biased estimation from the inclusion of outliers and inefficiency due to the deletion of uncontaminated observations. This analysis is followed by examples which illustrate the use of the interactive graphical analyses associated with the authors' FSDA toolbox. Numerical comparisons of the size and power of outlier tests appear in Chapter 5. Later chapters illustrate applications to response transformation in regression and to non-parametric regression. Extensions of the robust multiple regression model include Bayesian, heteroskedastic, time series and compositional regression, together with the clustering of regression models. Finally, several approaches to model selection are investigated and robust analyses of regression data are presented that illustrate the use of the techniques introduced earlier.
Exercises are given at the end of each chapter, with solutions at the end of the book. The MATLAB code can be reproduced using MATLAB Online, without the need for a license, or via the language-agnostic Jupyter notebook environment, after installing the MATLAB kernel. Online computer code is available for all examples and exercises, together with a series of YouTube videos.
Aimed at professional statisticians and researchers concerned with insightful data analysis, as well as postgraduate students, the book may also serve as a text for a modern interactive robust regression course.
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Persons
Anthony C. Atkinson
is Emeritus Professor of Statistics at the London School of Economics and Political Science, UK. He is a former Joint Editor of the Journal of the Royal Statistical Society, Series B and Associate Editor of Biometrika. He is the author of more than 270 papers published in international journals of statistics and six books published by Springer, Oxford University Press and Chapman and Hall.
Marco Riani
is a Full Professor of Statistics and the Director of the Robust Statistics Academy (Ro.S.A.), an interdepartmental center of the University of Parma, Italy. He is currently Associate Editor of Statistical Methods and Applications, Metron and STATS. He is the author of more than 200 publications and two books published by Springer. His research interests include robust statistics, regression, multivariate analysis and classification.
Aldo Corbellini
is an Associate Professor of Economic Statistics at the University of Parma, Italy. His research interests are in Bayesian robust regression and estimation, outlier detection in linear and generalized linear models and robust classification of functional data.
Domenico Perrotta
is a Researcher at the Joint Research Centre of the European Commission in Ispra, Italy. He holds a PhD in the Computational Theory of Automatic Learning from the École Normale Supérieure de Lyon, France. His research interests span the interface between computer science and statistics, including robust methods and their application to regression and clustering problems in the domain of anti-fraud and trade data analysis.
Valentin Todorov
worked as a Senior Management Information Officer at the United Nations Industrial Development Organization (UNIDO) in Vienna, Austria. He received a doctoral degree in statistics from Vienna University of Technology, Austria. His main research interests are in computational aspects of robust statistics, multivariate analysis, information systems and official statistics. He has (co-)developed and maintains several R packages on CRAN.
Content
Preface.- Introduction and the Grand Plan.- Introduction to M-Estimation for Univariate Samples.- Robust Estimators in Multiple Regression.- The Monitoring Approach in Multiple Regression.- Practical Comparison of the Different Estimators.- Transformations.- Non-parametric Regression.- Extensions of the Multiple Regression Model.- Model selection.- Some Robust Data Analyses.- Software and Datasets.- Solutions.- References.- Author Index.