Find out how to access previewonly content
Computing least trimmed squares regression with the forward search
 A. C. Atkinson,
 T.C. Cheng
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
Least trimmed squares (LTS) provides a parametric family of high breakdown estimators in regression with better asymptotic properties than least median of squares (LMS) estimators. We adapt the forward search algorithm of Atkinson (1994) to LTS and provide methods for determining the amount of data to be trimmed. We examine the efficiency of different trimming proportions by simulation and demonstrate the increasing efficiency of parameter estimation as larger proportions of data are fitted using the LTS criterion. Some standard data examples are analysed. One shows that LTS provides more stable solutions than LMS.
 Atkinson, A. C. (1985) Plots, Transformations and Regression, Oxford: Oxford University Press.
 Atkinson, A. C. (1994) Fast very robust methods for the detection of multiple outliers. Journal of the American Statistical Association, 89, 1329–1339.
 Atkinson, A. C. and Mulira, H.M. (1993) The stalactite plot for the detection of multivariate outliers. Statistics and Computing, 3, 27–35.
 Coakley, C. W., Mili, L. and Cheniae, M. G. (1994) Effect of leverage on the finite sample effciencies of high breakdown estimators. Statistics and Probability Letters, 19, 399–408.
 Croux, C., Rousseeuw, P. J. and Hössjer, O. (1994) Generalized Sestimators. Journal of the American Statistical Association, 89, 1271–1281.
 Davies, L. (1994) Desirable properties, breakdown and effciency in the linear regression model. Statistics and Probability Letters, 19, 361–370.
 Davies, P. L. (1993) Aspects of robust linear regression. The Annals of Statistics, 21, 1843–1899.
 Hadi, A. S. and Luceño, A. (1997) Maximum trimmed likelihood estimators: a unified approach, examples, and algorithms. Computational Statistics and Data Analysis, 25, 251–272.
 Hawkins, D. M. (1994) The feasible solution algorithm for least trimmed squares regression. Computational Statistics and Data Analysis, 17, 185–196.
 Hettmansperger, T. P. and McKean, J. W. (1998) Robust Nonparametric Statistical Methods, London: Arnold.
 Hettmansperger, T. P. and Sheather, S. J. (1992) A cautionary note on the method of the least median squares. The American Statistician, 46, 79–83.
 Hettmansperger, T. P. and Sheather, S. J. (1993) Reply to the comment of Rousseeuw, P. J., The American Statistician, 47, 162–163.
 Hössjer, O. (1994) Rankbased estimates in the linear model With high breakdown point. Journal of the American Statistical Association, 89, 149–157.
 Hössjer, O. (1995) Exact computation of the least trimmed squares estimate in simple linear regression. Computational Statistics and Data Analysis, 19, 265–282.
 Morgenthaler, S. (1991) A note on effcient regression estimators with positive breakdown point. Statistics and Probability Letters, 11, 469–472.
 Rousseeuw, P. J. (1984) Least median of squares regression. Journal of the American Statistical Association, 79, 871–880.
 Rousseeuw, P. J. (1993) Comment on the paper of Hettmansperger, T. P. and Sheather, S. J., The American Statistician, 47, 162.
 Rousseeuw, P. J. (1994) Unconventional features of positivebreakdown estimators. Statistics and Probability Letters, 19, 417–431.
 Rousseeuw, P. J. and Leroy, A. M. (1987) Robust Regression and Outlier Detection, New York: John Wiley.
 Stefanski, L. A. (1991) A note on high breakdown point estimators. Statistics and Probability Letters, 11, 353–358.
 Yohai, V. J. (1987) High breakdown point and high effciency robust estimators for regression. The Annals of Statistics, 15, 462–656.
 Yohai, V. J. and Zamar, R. H. (1988) High breakdown point estimates of regression by means of the minimization of an effcient scale. Journal of the American Statistical Association, 83, 406–413.
 Title
 Computing least trimmed squares regression with the forward search
 Journal

Statistics and Computing
Volume 9, Issue 4 , pp 251263
 Cover Date
 19991101
 DOI
 10.1023/A:1008942604045
 Print ISSN
 09603174
 Online ISSN
 15731375
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Detection of outliers
 forward search algorithm
 high breakdown point
 least trimmed squares
 regression diagnostics
 stalactite plot
 Industry Sectors
 Authors