Riani, Marco; Cerioli, Andrea; Atkinson, Anthony C.; Perrotta, Domenico Monitoring robust regression. (English) Zbl 1348.62200 Electron. J. Stat. 8, No. 1, 646-677 (2014). Summary: Robust methods are little applied (although much studied by statisticians). We monitor very robust regression by looking at the behaviour of residuals and test statistics as we smoothly change the robustness of parameter estimation from a breakdown point of 50% to non-robust least squares. The resulting procedure provides insight into the structure of the data including outliers and the presence of more than one population. Monitoring overcomes the hindrances to the routine adoption of robust methods, being informative about the choice between the various robust procedures. Methods tuned to give nominal high efficiency fail with our most complicated example. We find that the most informative analyses come from S estimates combined with Tukey’s biweight or with the optimal \(\rho\) functions. { } For our major example with 1,949 observations and 13 explanatory variables, we combine robust S estimation with regression using the forward search, so obtaining an understanding of the importance of individual observations, which is missing from standard robust procedures. We discover that the data come from two different populations. They also contain six outliers. { } Our analyses are accompanied by numerous graphs. Algebraic results are contained in two appendices, the second of which provides useful new results on the absolute odd moments of elliptically truncated multivariate normal random variables. Cited in 21 Documents MSC: 62J05 Linear regression; mixed models 62J20 Diagnostics, and linear inference and regression 62G35 Nonparametric robustness 62P20 Applications of statistics to economics Keywords:forward search; graphical methods; least trimmed squares; outliers; regression diagnostics; \(\rho\) function; S estimation; truncated normal distribution Software:robustbase; FSDA PDFBibTeX XMLCite \textit{M. Riani} et al., Electron. J. Stat. 8, No. 1, 646--677 (2014; Zbl 1348.62200) Full Text: DOI Euclid References: [1] Andrews, D. F., Bickel, P. J., Hampel, F. R., Tukey, W. J., and Huber, P. J. (1972)., Robust Estimates of Location: Survey and Advances . Princeton University Press, Princeton, NJ. · Zbl 0254.62001 [2] Atkinson, A. C. and Riani, M. (2000)., Robust Diagnostic Regression Analysis . Springer-Verlag, New York. · Zbl 0964.62063 [3] Atkinson, A. C. and Riani, M. (2002). 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