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2014 Monitoring robust regression
Marco Riani, Andrea Cerioli, Anthony C. Atkinson, Domenico Perrotta
Electron. J. Statist. 8(1): 646-677 (2014). DOI: 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 $\rho$ 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.

Citation

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Marco Riani. Andrea Cerioli. Anthony C. Atkinson. Domenico Perrotta. "Monitoring robust regression." Electron. J. Statist. 8 (1) 646 - 677, 2014. https://doi.org/10.1214/14-EJS897

Information

Published: 2014
First available in Project Euclid: 20 May 2014

zbMATH: 1348.62200
MathSciNet: MR3211027
Digital Object Identifier: 10.1214/14-EJS897

Subjects:
Primary: 62G35, 62J05, 62J20
Secondary: 62P20

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.8 • No. 1 • 2014
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