Abstract
A fast algorithm is presented for robust estimation of a linear model with a distributed intercept. This is a regression model in which the data set contains groups with the same slopes but different intercepts, a situation which often occurs in economics. In each group, the algorithm first looks for outliers in (x,y) -space by means of a robust projection method. Then a modified version of the resampling technique is applied to the whole data set, in order to find an approximation to least median of squares or other regression methods with a positive breakdown point. Because of the preliminary projections, the number of subsets may be drastically reduced. Simulations and examples show that the overall computation time is substantially lower than that of the straightforward algorithm. The method is illustrated with a real data set.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Armstrong, R.D. and Frome, E.L. (1977): A special purpose linear programming algorithm for obtaining least absolute value estimators in a linear model with dummy variables. Communications in Statistics: Simulation and Computation B 6 383–398.
Chatterjee, S. and Price, B. (1977): Regression Analysis by Example. John Wiley, New York.
Donoho, D.L. and Gasko, M. (1992): Breakdown properties of location estimates based on halfspace depth and projected outlyingness. Ann. Statist. 20 1803–1827.
Draper, N.R. and Smith, H. (1981): Applied Regression Analysis. John Wiley, New York.
Edwards, A.L. (1985): Multiple Regression and the Analysis of Variance and Covariance. W.H. Freeman and Company, New York.
Mincer, J. (1974): Schooling, Experience and Earnings. Columbia University Press, New York.
Montgomery, D.C. (1991): Design and Analysis of Experiments. John Wiley, New York.
Montgomery, D.C. and Peck, A.E. (1982): Introduction to Linear Regression Analysis. John Wiley, New York.
Rousseeuw, P.J. (1984): Least median of squares regression. J. Amer. Statist. Assoc. 79 871–880.
Rousseeuw, P.J. and Leroy, A.M. (1987): Robust Regression and Outlier Detection. John Wiley, New York.
Rousseeuw, P.J. and Wagner, J. (1994): Robust regression with a distributed intercept using least median of squares. Comput. Statist. & Data Analysis 17 65–76.
Rousseeuw, P.J. and van Zomeren, B.C. (1990): Unmasking multivariate outliers and leverage points. J. Amer. Statist. Assoc. 85 633–639.
Rousseeuw, P.J. and van Zomeren, B.C. (1992): A comparison of some quick algorithms for robust regression. Comput. Statist. & Data Analysis 15 107–116.
Wagner, J. (1990): Sektorlohndifferentiale in der Bundesrepublik Deutschland: Empirische Befunde und ökonometrische Untersuchungen zu theoretischen Erklärungen. Discussion Paper No. 154, Fachbereich Wirtschaftswissenschaften, Universität Hannover.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Huber, M., Rousseeuw, P.J. (1996). Robust Regression with a Categorical Covariable. In: Rieder, H. (eds) Robust Statistics, Data Analysis, and Computer Intensive Methods. Lecture Notes in Statistics, vol 109. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2380-1_14
Download citation
DOI: https://doi.org/10.1007/978-1-4612-2380-1_14
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94660-3
Online ISBN: 978-1-4612-2380-1
eBook Packages: Springer Book Archive