README.md

Chapter 4 The Monitoring Approach in Multiple Regression

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Atkinson,A.C., Riani,M., Corbellini,A., Perrotta D., and Todorov,V. (2024), "Applied Robust Statistics through the Monitoring Approach: Applications in Regression", Heidelberg: Springer Nature.

Abstract

This chapter introduces algorithms for the monitoring approach to robust statistical analysis and compares their performance in the analyses of several sets of data. The Forward Search (FS) is introduced in section 4.1. This algorithm fits subsets of the data of increasing size in such a way that the most outlying observations are included towards the end of the search. To monitor other forms of robust regression, we estimate the parameters using, typically, a grid of 50 values of bdp or eff. Monitoring plots of residuals, parameter estimates and $t$-tests from very robust regression to LS are introduced in section 4.6; these plots are enriched by brushing and linking to other plots. Frequently, the plots from monitoring residuals show an abrupt change from robust to LS analyses. In section 4.7 we introduce the empirical bdp defining the most efficient robust estimator for each dataset, thus overcoming the arbitrariness of the conventional approach to robust statistics. Many examples are given in section 4.9 for a variety of estimators. The chapter concludes in section 4.11 with a generalized Bayesian Information Criterion (BIC) for model choice which, via the mean shift outlier model, makes it possible to compare models in which different numbers of observations have been deleted.

Code to reproduce Figures and Tables in this Chapter

FileName	Description	Open in MATLAB on line	Jupiter notebook
ARregression.m	AR regression data This file creates Figures 4.15-4.22		[ipynb]
ARregressionInteractive.m	AR regression data This file creates Figures 4.12-4.14 Note that this file needs interactivity		[ipynb]
Bank.m	Bank data This file creates Figure 4.34-4.42.		[ipynb]
BankInteractive.m	Bank data This file creates Figure 4.35 and 4.36.		[ipynb]
Hawkins.m	Hawkins data This file creates Figure 4.23 and Figures 4.27-4.29		[ipynb]
HawkinsInteractive.m	Hawkins data (interactive part). This file creates Figures 4.24-4.26. Note that this file needs interactivity.		[ipynb]
MentalIllness.m	Contaminated illness data. This file creates Figure 4.43.		[ipynb]
Stars.m	Stars data. This file creates Figures 4.1-4.4, 4.9-4.11		[ipynb]
SurgicalUnit.m	Surgical Unit data. This file creates Figures 4.30-4.33.		[ipynb]
Wool.m	Wool data. This file creates Figures 4.5-4.8.		[ipynb]