Monitoring robust regression

We show how to 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 functions. We demonstrate the monitoring of robust regression for three data sets of increasingly complex nature. For our major example, with 1,949 observations and 13 explanatory variables, we combined 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 and contain six outliers.

RIANI Marco;  CERIOLI Andrea;  ATKINSON Anthony C.; 

PERROTTA Domenico; 

2015-01-22

CMStatistics and CFEnetwork

JRC91723

978-84-937822-4-5,   

https://publications.jrc.ec.europa.eu/repository/handle/JRC91723,