Article
Full entry |
PDF
(0.6 MB)
Feedback
PDF
(0.6 MB)
Feedback
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
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.
References:
[1] Andrews, D. F.: Robust Estimates of Location: Survey and Advances. Princeton University Press, Princeton, N.Y., 1972. MR 0331595 | Zbl 0254.62001
[2] Atkinson, A. C., Cheng, T. C.: Computing least trimmed squares regression with forward search. Statistics and Computing 9 (1998), 251–263. DOI 10.1023/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.
[4] Hampel, F. R. et al.: Robust Statistics: The Approach Based on Influence Functions. Wiley Series in Probability and Statistics, Wiley, 1986. MR 0829458 | Zbl 0593.62027
[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
[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 10.1016/S0167-9473(99)00029-8
[7] Koenker, R., Bassett, G.: Regression quantiles. Econometrica 46 (1978), 466–476. DOI 10.2307/1913643 | MR 0474644 | Zbl 0373.62038
[8] Koenker, R.: Quantile Regression. Cambridge University Press, Cambridge, 2005. MR 2268657 | Zbl 1111.62037
[9] Rousseeuw, P. J.: Least median of squares regression. Journal of The American Statistical Association 79 (1984), 871–880. DOI 10.1080/01621459.1984.10477105 | MR 0770281 | Zbl 0551.62049
[10] Ruppert, D., Carroll, J.: Trimmed Least Squares Estimation in the Linear Model. Journal of the American Statistical Association75 (1980), 828–838. DOI 10.1080/01621459.1980.10477560 | MR 0600964 | Zbl 0459.62055
[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 10.1016/0167-7152(94)90186-4 | MR 1278670 | Zbl 0803.62027
[12] Tableman, M.: The asymptotics of the least trimmed absolute deviations (LTAD) estimator. Statistics & Probability Letters 19 (1994), 387–398. DOI 10.1016/0167-7152(94)90007-8 | MR 1278675 | Zbl 0797.62029
Search
Partner of
