LEADER 05403nam 22006615 450 001 9911016278603321 005 20250727130209.0 010 $a3-031-88365-9 024 7 $a10.1007/978-3-031-88365-1 035 $a(CKB)39767189500041 035 $a(DE-He213)978-3-031-88365-1 035 $a(MiAaPQ)EBC32260876 035 $a(Au-PeEL)EBL32260876 035 $a(EXLCZ)9939767189500041 100 $a20250727d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRobust Statistics Through the Monitoring Approach $eApplications in Regression /$fby Anthony C. Atkinson, Marco Riani, Aldo Corbellini, Domenico Perrotta, Valentin Todorov 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (XXVII, 546 p. 358 illus., 354 illus. in color.) 225 1 $aSpringer Series in Statistics,$x2197-568X 311 08$a3-031-88364-0 327 $aPreface -- 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. 330 $aThis 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. . 410 0$aSpringer Series in Statistics,$x2197-568X 606 $aStatistics 606 $aStatistics 606 $aMathematical statistics$xData processing 606 $aRegression analysis 606 $aStatistical Theory and Methods 606 $aApplied Statistics 606 $aStatistics and Computing 606 $aLinear Models and Regression 615 0$aStatistics. 615 0$aStatistics. 615 0$aMathematical statistics$xData processing. 615 0$aRegression analysis. 615 14$aStatistical Theory and Methods. 615 24$aApplied Statistics. 615 24$aStatistics and Computing. 615 24$aLinear Models and Regression. 676 $a519.5 700 $aAtkinson$b Anthony C$4aut$4http://id.loc.gov/vocabulary/relators/aut$0102940 702 $aRiani$b Marco$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aCorbellini$b Aldo$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aPerrotta$b Domenico$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aTodorov$b Valentin$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911016278603321 996 $aRobust Statistics Through the Monitoring Approach$94412335 997 $aUNINA