×

Trimmed estimators in regression framework. (English) Zbl 1244.62099

Summary: From the practical point of view 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 a special kind of methods based on trimming. There exist several approaches which use trimming off part of the observations, namely the well known high breakdown point method least trimmed squares, least trimmed absolute deviation estimators or, e.g., the regression \(L\)-estimate trimmed least squares of R. Koenker and G. Bassett [seeEconometrica 46, 33–50 (1978; Zbl 0373.62038)]. Our goal is to compare these methods and its properties in detail.

MSC:

62J05 Linear regression; mixed models
62G08 Nonparametric regression and quantile regression
62F10 Point estimation

Citations:

Zbl 0373.62038
PDF BibTeX XML Cite
Full Text: EuDML

References:

[1] Andrews, D. F.: Robust Estimates of Location: Survey and Advances. Princeton University Press, Princeton, N.Y., 1972. · 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.
[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. · 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.
[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. · Zbl 04556219
[7] Koenker, R., Bassett, G.: Regression quantiles. Econometrica 46 (1978), 466-476. · Zbl 0373.62038
[8] Koenker, R.: Quantile Regression. Cambridge University Press, Cambridge, 2005. · Zbl 1111.62037
[9] Rousseeuw, P. J.: Least median of squares regression. Journal of The American Statistical Association 79 (1984), 871-880. · 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. · 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. · Zbl 0803.62027
[12] Tableman, M.: The asymptotics of the least trimmed absolute deviations (LTAD) estimator. Statistics & Probability Letters 19 (1994), 387-398. · Zbl 0797.62029
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.