Consistency and asymptotic distribution of the Theil–Sen estimator

Peng, Hanxiang; Wang, Shaoli; Wang, Xueqin

doi:10.1016/j.jspi.2007.06.036

Cited by 53 publications

(29 citation statements)

References 19 publications

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“…Sen (1968) derives the asymptotic distribution of (16) under i.i.d. regression errors with a continuous distribution, while Peng et al (2008) analyze it under more general conditions on the distribution of the regression errors. But, to the best of our knowledge, there is no published result on the behavior of the Theil-Sen estimator when the regression errors are serially dependent.…”

Section: Rank Kpss For Trend Stationaritymentioning

confidence: 99%

Rank tests for short memory stationarity

Pelagatti

Sen

2013

Journal of Econometrics

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Section: Rank Kpss For Trend Stationaritymentioning

confidence: 99%

Rank tests for short memory stationarity

Pelagatti

Sen

2013

Journal of Econometrics

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“…Roughly, about 29% of the points must be changed in order to make the estimate of the slope arbitrarily large or small. Other asymptotic properties have been studied by Wang (2005) and Peng et al (2008). Akritas et al (1995) applied it to astronomical data and Fernandes and Leblanc (2005) to remote sensing.…”

Section: The Theil-sen Estimator and The Suggested Modificationmentioning

confidence: 99%

“…Akritas et al (1995) applied it to astronomical data and Fernandes and Leblanc (2005) to remote sensing. Although the bulk of the results on the Theil-Sen estimator deal with situations where the dependent variable is continuous, an exception is the paper by Peng et al (2008) that includes results when dealing a discontinuous error term. They show that when the distribution of the error term is discontinuous, the Theil-Sen estimator can be super-efficient.…”

Section: The Theil-sen Estimator and The Suggested Modificationmentioning

confidence: 99%

Robust Regression Estimators When There are Tied Values

Wilcox

Clark

2013

J. Mod. App. Stat. Meth.

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It is well known that when using the ordinary least squares regression estimator, outliers among the dependent variable can result in relatively poor power. Many robust regression estimators have been derived that address this problem, but the bulk of the results assume that the dependent variable is continuous. It is demonstrated that when there are tied values, several robust regression estimators can perform poorly in terms of controlling the Type I error probability, even with a large sample size. The presence of tied values does not necessarily mean that they perform poorly, but there is the issue of whether there is a robust estimator that performs reasonably well in situations where other estimators do not. The main result is that a modification of the Theil-Sen estimator achieves this goal. Results on the small-sample efficiency of the modified Theil-Sen estimator are reported as well. Data from the Well Elderly 2 Study, which motivated this study, are used to illustrate that the modified Theil-Sen estimator can make a practical difference.

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“…Despite the fact that such an estimator was proposed many years ago (Theil 1950;Sen 1968), recent literature shows a vivid interest in its application and development. The Theil-Sen estimator was indeed applied successfully, as an alternative to least-squares, in astronomy (Akritas, Murphy, and Lavalley 1995), in remote sensing (Fernandes and Leblanc 2005) and in genomics (Sen 2011); in addition, some recent papers dealt both with a deeper study of the properties of the Theil-Sen estimator (Wang and Yu 2005;Peng, Wang, and Wang 2008) and with its extension to other settings, such as the presence of censored data or heteroskedasticity (Akritas et al 1995;Wilcox 1998), the case of a quadratic regression (Chatterjee and Olkin 2006) and the multivariate linear model (Zhou and Serfling 2008).…”

Section: Introductionmentioning

confidence: 99%

Some maximum-indifference estimators for the slope of a univariate linear model

Borroni

Cifarelli

2016

Journal of Nonparametric Statistics

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As known, the least-squares estimator of the slope of a univariate linear model sets to zero the covariance between the regression residuals and the values of the explanatory variable. To prevent the estimation process from being influenced by outliers, which can be theoretically modelled by a heavy-tailed distribution for the error term, one can substitute covariance with some robust measures of association, for example Kendall's tau in the popular Theil-Sen estimator. In a scarcely known Italian paper, Cifarelli [(1978), 'La Stima del Coefficiente di Regressione Mediante l'Indice di Cograduazione di Gini', Rivista di matematica per le scienze economiche e sociali, 1, 7-38. A translation into English is available at http://arxiv.org/abs/1411.4809 and will appear in Decisions in Economics and Finance] shows that a gain of efficiency can be obtained by using Gini's cograduation index instead of Kendall's tau. This paper introduces a new estimator, derived from another association measure recently proposed. Such a measure is strongly related to Gini's cograduation index, as they are both built to vanish in the general framework of indifference. The newly proposed estimator is shown to be unbiased and asymptotically normally distributed. Moreover, all considered estimators are compared via their asymptotic relative efficiency and a small simulation study. Finally, some indications about the performance of the considered estimators in the presence of contaminated normal data are provided.

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Consistency and asymptotic distribution of the Theil–Sen estimator

Cited by 53 publications

References 19 publications

Rank tests for short memory stationarity

Rank tests for short memory stationarity

Robust Regression Estimators When There are Tied Values

Some maximum-indifference estimators for the slope of a univariate linear model

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