Discussion and Extensions

• 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: 25-26

call monitoring_S_MM_LTS_LMS("lib.books", "q" , "v", "S");

call monitoring_S_MM_LTS_LMS("lib.books", "q" , "v", "lts");

call monitoring_S_MM_LTS_LMS("lib.books", "q" , "v", "lms");

Figure 16: Books data; S,LTS and LMS estimators: monitoring the scaled residuals as the breakdown point

varies. At the foot of each panel, the code used to generate the plot.

clear lower linear relationship is f‌itted, initially to observations near the origin with a low variance. As bdp

decreases fewer observations are trimmed or downweighted and those with higher variance further from the

origin inf‌luence the f‌it, increasing the estimate of σ2and decreasing the values of the residuals. That most

of the residuals are positive until a bdp around 8% is caused by the (basically) two clouds of observations

that lie above the line that is being robustly f‌itted.

13. Discussion and Extensions

The main purpose of the SAS programming described in this paper is to provide a library of routines for very

robust regression and to embed these in a monitoring framework. As a result adaptive values of trimming

parameters or bdp can be found which, for a particular dataset, yield the most ef‌f‌icient robust parameter

estimates. We also provide a series of innovative plots to aid interpretation of the data and also of the f‌itted

models and their robustness. In doing so, we have introduced two new monitoring possibilities, for LTS and

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