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Monitoring robust regression

Riani, Marco, Cerioli, Andrea, Atkinson, Anthony C. and Perrotta, Domenico (2014) Monitoring robust regression. Electronic Journal of Statistics, 8. pp. 646-677. ISSN 1935-7524

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Identification Number: 10.1214/14-EJS897

Abstract

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 ρ 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.

Item Type: Article
Official URL: http://projecteuclid.org/
Additional Information: © 2014 Institute of Mathematical Statistics
Divisions: Statistics
Subjects: G Geography. Anthropology. Recreation > GA Mathematical geography. Cartography
JEL classification: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C42 - Survey Methods
C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C44 - Statistical Decision Theory; Operations Research
Sets: Departments > Statistics
Date Deposited: 08 Jul 2014 11:53
Last Modified: 20 Jun 2019 01:56
Funders: MIUR PRIN
URI: http://eprints.lse.ac.uk/id/eprint/57552

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