Monitoring Other Forms of Robust Regression

• Author: Francesca Torti - Marco Riani - Anthony C. Atkinson - Domenico Perrotta - Aldo Corbellini
• Profession: European Commission, Joint Research Centre (JRC) - University of Parma, Italy - London School of Economics, UK - European Commission, Joint Research Centre (JRC) - University of Parma, Italy
• Pages: 21-24

99%

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1%

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CALL FSR("lib.loyalty", {’x1’ ’x2’ ’x3’}, "y", "CLASSIFY mdrplot ")

transform_original_data = 0 ;

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CALL FSR("lib.loyalty", {’x1’ ’x2’ ’x3’}, "y", "CLASSIFY RESFWDPLOT ")

transform_original_data = 0 ;

Figure 12: Loyalty card data: monitoring plots for log-transformed data (λ= 0). The top panel shows the

absolute values of minimum deletion residuals among observations not in the subset, with the last part of the

trajectory corresponding to the 14 detected outliers, automatically highlighted in red (in the on-line .pdf version).

The bottom panel shows the scaled residuals with the trajectories corresponding to the 14 detected outliers

automatically represented in red (in the on-line .pdf version). The box under each panel contains the SAS code

used to generate the plot.

beta coef‌f‌icients (Figures 14, Figures 4 and 10) we have calculated the coef‌f‌icients using z(λ)as the response

so that the numerical values of the coef‌f‌icients are comparable across λvalues.

11. Monitoring Other Forms of Robust Regression

11.1. Soft Trimming

In addition to the extension of the SAS version of the FS to include the batch procedure of §8 we have

provided a SAS version of the monitoring of S-estimation, which is also available in FSDA. Further we have

introduced to SAS two new monitoring possibilities, those for LTS and LMS regression, which are not present

in the FSDA toolbox. In this sec tion we provide brief comments on robust regression with both soft and

hard trimming. Our SAS examples are in §12. A much fuller discussion of monitoring robust regression is

Riani et al. (2014a), including examples of S, MM, LMS and LTS analyses using the FSDA. We monitor

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