Trimmed Estimators in Regression Framework

TomĂĄĹĄ Jurczyk

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2011)

  • Volume: 50, Issue: 2, page 45-53
  • ISSN: 0231-9721

Abstract

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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.

How to cite

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Jurczyk, TomĂĄĹĄ. "Trimmed Estimators in Regression Framework." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 50.2 (2011): 45-53. <http://eudml.org/doc/196760>.

@article{Jurczyk2011,
abstract = {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.},
author = {Jurczyk, TomĂĄĹĄ},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {trimmed mean; least trimmed squares; least trimmed absolute deviations; trimmed LSE; regression quantiles; trimmed mean; least trimmed squares; least trimmed absolute deviations; trimmed LSE; regression quantiles},
language = {eng},
number = {2},
pages = {45-53},
publisher = {Palacký University Olomouc},
title = {Trimmed Estimators in Regression Framework},
url = {http://eudml.org/doc/196760},
volume = {50},
year = {2011},
}

TY - JOUR
AU - Jurczyk, TomĂĄĹĄ
TI - Trimmed Estimators in Regression Framework
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2011
PB - Palacký University Olomouc
VL - 50
IS - 2
SP - 45
EP - 53
AB - 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.
LA - eng
KW - trimmed mean; least trimmed squares; least trimmed absolute deviations; trimmed LSE; regression quantiles; trimmed mean; least trimmed squares; least trimmed absolute deviations; trimmed LSE; regression quantiles
UR - http://eudml.org/doc/196760
ER -

References

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  1. Andrews, D. F., Robust Estimates of Location: Survey and Advances, Princeton University Press, Princeton, N.Y., 1972. (1972) Zbl0254.62001MR0331595
  2. Atkinson, A. C., Cheng, T. C., 10.1023/A:1008942604045, Statistics and Computing 9 (1998), 251–263. (1998) DOI10.1023/A:1008942604045
  3. Čížek, P., Asymptotics of the trimmed least squares, Journal of Statistical Planning and Inference, CentER DP series 2004/72 (2004), 1–53. (2004) 
  4. Hampel, F. R. et al., Robust Statistics: The Approach Based on Influence Functions, Wiley Series in Probability and Statistics, Wiley, 1986. (1986) Zbl0593.62027MR0829458
  5. Hettmansperger, T. P., Sheather, S. J., A Cautionary Note on the Method of Least Median Squares, The American Statistician 46 (1991), 79–83. (1991) MR1165565
  6. Hawkins, D. M., Olive, D., 10.1016/S0167-9473(99)00029-8, Computational Statistics & Data Analysis 32, 2 (1999), 119–134. (1999) DOI10.1016/S0167-9473(99)00029-8
  7. Koenker, R., Bassett, G., 10.2307/1913643, Econometrica 46 (1978), 466–476. (1978) Zbl0373.62038MR0474644DOI10.2307/1913643
  8. Koenker, R., Quantile Regression, Cambridge University Press, Cambridge, 2005. (2005) Zbl1111.62037MR2268657
  9. Rousseeuw, P. J., 10.1080/01621459.1984.10477105, Journal of The American Statistical Association 79 (1984), 871–880. (1984) Zbl0551.62049MR0770281DOI10.1080/01621459.1984.10477105
  10. Ruppert, D., Carroll, J., 10.1080/01621459.1980.10477560, Journal of the American Statistical Association75 (1980), 828–838. (1980) Zbl0459.62055MR0600964DOI10.1080/01621459.1980.10477560
  11. Tableman, M., 10.1016/0167-7152(94)90186-4, Statistics & Probability Letters 19 (1994), 329–337. (1994) Zbl0803.62027MR1278670DOI10.1016/0167-7152(94)90186-4
  12. Tableman, M., 10.1016/0167-7152(94)90007-8, Statistics & Probability Letters 19 (1994), 387–398. (1994) Zbl0797.62029MR1278675DOI10.1016/0167-7152(94)90007-8

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