Robust regression trees based on M-estimators

Authors

  • Giuliano Galimberti Alma Mater Studiorum - Università di Bologna
  • Marilena Pillati Alma Mater Studiorum - Università di Bologna
  • Gabriele Soffritti Alma Mater Studiorum - Università di Bologna

DOI:

https://doi.org/10.6092/issn.1973-2201/3503

Abstract

The paper addresses the problem of robustness of regression trees with respect to outlying values in the dependent variable. New robust tree-based procedures are described, which are obtained by introducing in the tree building phase some objective functions already used in the linear robust regression approach, namely Huber’s and Tukey’s bisquare functions. The performance of the new procedures is evaluated through a Monte Carlo experiment.

References

J.N. ADICHIE (1967), Estimates of regression parameters based on rank tests, “The Annals of Mathematical Statistics”, 38, pp. 894-904.

A. ATKINSON, M. RIANI (2000), Robust Diagnostic Regression Analysis. Springer, New York.

L. BRIEMAN, J. FRIEDMAN, R. OLSHEN, C. STONE (1984), Classification and regression trees. Wadsworth, Belmont.

R. CHAMBERS, A. HENTGES, X. ZHAO (2004), Robust automatic methods for outlier and error detection, “Journal of the Royal Statistical Society”, A, 167, pp. 323-339.

M. COSTA, G. GALIMBERTI, A. MONTANARI (2006), Binary segmentation methods based on Gini index: a new approach to the multidensional analysis of income inequalities, “Statistica & Applicazioni”, IV, pp. 19-37.

R.V. HOGG, R.H. RANDLES (1975), Adaptive distribution-free regression methods and their applications, “Technometrics”, 17, pp. 399-407.

F.R. HAMPEL (1974), The influence curve and its role in robust estimation, “Journal of the American Statistical Association”, 69, pp. 383-393.

P.J. HUBER (1964), Robust estimation of a local parameter, “The Annals of Mathematical Statistics”, 35, pp. 73-101.

P.J. HUBER (1981), Robust Statistics, Wiley, New York.

P.J. HUBER (1984), Finite sample breakdown of M- and P-estimators, “Annals of Statistics”, 12, pp. 119-126.

L.A. JAECKEL (1972), Estimating regression coefficients by minimizing the dispersion of the residuals, “The Annals of Mathematical Statistics”, 43, pp. 1449-1458.

J. JUREČKOVÁ (1977), Asymptotic relations of M-estimates and R-estimates in linear regression models, “Annals of Statistics”, 5, pp. 464-472.

J. JUREČKOVÁ, J. PICEK (2006), Robust Statistical Methods with R. Chapman & Hall/CRC, Boca Raton.

R. KOENKER, G.J. BASSETT (1978), Regression quantiles, “Econometrica”, 46, pp. 33-50.

R. KOENKER, P. HAMMOND, A. HOLLY (EDS.) (2005), Quantile Regression, Cambridge University Press, Cambridge.

R.A. MARONNA, R.D. MARTIN, V.J. YOHAI (2006), Robust Statistics. Theory and Methods, Wiley, New York.

D.C. MONTGOMERY, E.A. PECK, G.G. VINING (2006), Introduction to Linear Regression Analysis, Fourth edition. Wiley, New York.

P.J. ROUSSEEUW (1984), Least median of squares regression, “Journal of the American Statistical Association”, 79, pp. 871-880.

P.J. ROUSSEEUW, A.M. LEROY (1987), Robust Regression and Outlier Detection. Wiley, New York.

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Published

2007-06-30

How to Cite

Galimberti, G., Pillati, M., & Soffritti, G. (2007). Robust regression trees based on M-estimators. Statistica, 67(2), 173–190. https://doi.org/10.6092/issn.1973-2201/3503

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Section

Articles