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Title: Trimmed Estimators in Regression Framework (English)
Author: Jurczyk, Tomáš
Language: English
Journal: Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
ISSN: 0231-9721
Volume: 50
Issue: 2
Year: 2011
Pages: 45-53
Summary lang: English
Category: math
Summary: From the practical point of view the regression analysis and its Least Squares method is clearly one of the most used techniques of statistics. Unfortunately, if there is some problem present in the data (for example contamination), classical methods are not longer suitable. A lot of methods have been proposed to overcome these problematic situations. In this contribution we focus on special kind of methods based on trimming. There exist several approaches which use trimming off part of the observations, namely well known high breakdown point method the Least Trimmed Squares, Least Trimmed Absolute Deviation estimator or e.g. regression $L$-estimate Trimmed Least Squares of Koenker and Bassett. Our goal is to compare these methods and its properties in detail. (English)
Keyword: trimmed mean
Keyword: least trimmed squares
Keyword: least trimmed absolute deviations
Keyword: trimmed LSE
Keyword: regression quantiles
MSC: 62J05
MSC: 62J20
idZBL: Zbl 1244.62099
idMR: MR2920707
Date available: 2011-12-16T14:46:58Z
Last updated: 2013-09-18
Stable URL:
Reference: [1] Andrews, D. F.: Robust Estimates of Location: Survey and Advances. Princeton University Press, Princeton, N.Y., 1972. Zbl 0254.62001, MR 0331595
Reference: [2] Atkinson, A. C., Cheng, T. C.: Computing least trimmed squares regression with forward search. Statistics and Computing 9 (1998), 251–263. 10.1023/A:1008942604045
Reference: [3] Čížek, P.: Asymptotics of the trimmed least squares. Journal of Statistical Planning and Inference, CentER DP series 2004/72 (2004), 1–53.
Reference: [4] Hampel, F. R. et al.: Robust Statistics: The Approach Based on Influence Functions. Wiley Series in Probability and Statistics, Wiley, 1986. Zbl 0593.62027, MR 0829458
Reference: [5] Hettmansperger, T. P., Sheather, S. J.: A Cautionary Note on the Method of Least Median Squares. The American Statistician 46 (1991), 79–83. MR 1165565
Reference: [6] Hawkins, D. M., Olive, D.: Applications and algorithms for least trimmed sum of absolute deviations regression. Computational Statistics & Data Analysis 32, 2 (1999), 119–134. 10.1016/S0167-9473(99)00029-8
Reference: [7] Koenker, R., Bassett, G.: Regression quantiles. Econometrica 46 (1978), 466–476. Zbl 0373.62038, MR 0474644, 10.2307/1913643
Reference: [8] Koenker, R.: Quantile Regression. Cambridge University Press, Cambridge, 2005. Zbl 1111.62037, MR 2268657
Reference: [9] Rousseeuw, P. J.: Least median of squares regression. Journal of The American Statistical Association 79 (1984), 871–880. Zbl 0551.62049, MR 0770281, 10.1080/01621459.1984.10477105
Reference: [10] Ruppert, D., Carroll, J.: Trimmed Least Squares Estimation in the Linear Model. Journal of the American Statistical Association75 (1980), 828–838. Zbl 0459.62055, MR 0600964, 10.1080/01621459.1980.10477560
Reference: [11] Tableman, M.: The influence functions for the least trimmed squares and the least trimmed absolute deviations estimators. Statistics & Probability Letters 19 (1994), 329–337. Zbl 0803.62027, MR 1278670, 10.1016/0167-7152(94)90186-4
Reference: [12] Tableman, M.: The asymptotics of the least trimmed absolute deviations (LTAD) estimator. Statistics & Probability Letters 19 (1994), 387–398. Zbl 0797.62029, MR 1278675, 10.1016/0167-7152(94)90007-8


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