Geodesic
Trimmed Estimators in Regression Framework
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 2, pp. 45-53 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 62J05, 62J20
Keywords: trimmed mean; least trimmed squares; least trimmed absolute deviations; trimmed LSE; regression quantiles 
@article{AUPO_2011_50_2_a5,
     author = {Jurczyk, Tom\'a\v{s}},
     title = {Trimmed {Estimators} in {Regression} {Framework}},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
     pages = {45--53},
     year = {2011},
     volume = {50},
     number = {2},
     mrnumber = {2920707},
     zbl = {1244.62099},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPO_2011_50_2_a5/}
}
TY  - JOUR
AU  - Jurczyk, Tomáš
TI  - Trimmed Estimators in Regression Framework
JO  - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY  - 2011
SP  - 45
EP  - 53
VL  - 50
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AUPO_2011_50_2_a5/
LA  - en
ID  - AUPO_2011_50_2_a5
ER  - 
%0 Journal Article
%A Jurczyk, Tomáš
%T Trimmed Estimators in Regression Framework
%J Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
%D 2011
%P 45-53
%V 50
%N 2
%U http://geodesic.mathdoc.fr/item/AUPO_2011_50_2_a5/
%G en
%F AUPO_2011_50_2_a5
Jurczyk, Tomáš. Trimmed Estimators in Regression Framework. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 2, pp. 45-53. http://geodesic.mathdoc.fr/item/AUPO_2011_50_2_a5/

[1] Andrews, D. F.: Robust Estimates of Location: Survey and Advances. Princeton University Press, Princeton, N.Y., 1972. | MR | Zbl

[2] Atkinson, A. C., Cheng, T. C.: Computing least trimmed squares regression with forward search. Statistics and Computing 9 (1998), 251–263. | DOI

[3] Čížek, P.: Asymptotics of the trimmed least squares. Journal of Statistical Planning and Inference, CentER DP series 2004/72 (2004), 1–53.

[4] Hampel, F. R. et al.: Robust Statistics: The Approach Based on Influence Functions. Wiley Series in Probability and Statistics, Wiley, 1986. | MR | Zbl

[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

[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. | DOI

[7] Koenker, R., Bassett, G.: Regression quantiles. Econometrica 46 (1978), 466–476. | DOI | MR | Zbl

[8] Koenker, R.: Quantile Regression. Cambridge University Press, Cambridge, 2005. | MR | Zbl

[9] Rousseeuw, P. J.: Least median of squares regression. Journal of The American Statistical Association 79 (1984), 871–880. | DOI | MR | Zbl

[10] Ruppert, D., Carroll, J.: Trimmed Least Squares Estimation in the Linear Model. Journal of the American Statistical Association75 (1980), 828–838. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[12] Tableman, M.: The asymptotics of the least trimmed absolute deviations (LTAD) estimator. Statistics & Probability Letters 19 (1994), 387–398. | DOI | MR | Zbl