Tail Behavior of Regression Estimators and their Breakdown Points
Copyright policy )Tail Behavior of Regression Estimators and their Breakdown Points
Following \textit{J. Jurečková} [Ann. Stat. 9, 578-585 (1981; Zbl 0476.62032), and Commentat. Math. Univ. Carol. 22, 365-375 (1981; Zbl 0466.62030)], this paper introduces a finite-sample measure of performance of regression estimators based on tail behaviour. The least squares estimator is studied in detail; it is found that it achieves good tail performance under strictly Gaussian condition, but it is extremly poor in the case of heavy-tail error distributions. Further, the tail behaviour of various robust estimators of the parameters of linear models, such as \(L_ 1\)-estimates and \(M\)-estimates, is studied. It also is shown that the finite-sample measure of tail performance is essentially the same as the finite sample concept of breakdown point introduced by \textit{D. L. Donoho} and \textit{P. J. Huber} [Festschr. for Erich L. Lehmann, 157-184 (1983; Zbl 0523.62032)].
- Charles University Czech Republic
- University of Illinois System United States
Linear regression; mixed models, heavy-tail error distributions, robust estimators, Point estimation, least squares estimator, robustness, breakdown point, tail behaviour, strictly Gaussian, finite-sample measure of performance of regression estimators, Robustness and adaptive procedures (parametric inference), linear models, M-estimates
Linear regression; mixed models, heavy-tail error distributions, robust estimators, Point estimation, least squares estimator, robustness, breakdown point, tail behaviour, strictly Gaussian, finite-sample measure of performance of regression estimators, Robustness and adaptive procedures (parametric inference), linear models, M-estimates
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).61 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 1% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!