The Experts below are selected from a list of 72 Experts worldwide ranked by ideXlab platform
Rand R. Wilcox - One of the best experts on this subject based on the ideXlab platform.
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Some results on extensions and modifications of the Theil-Sen regression Estimator.
The British journal of mathematical and statistical psychology, 2004Co-Authors: Rand R. WilcoxAbstract:Many robust regression Estimators have been proposed that have a high, finite-sample breakdown point, roughly meaning that a large proportion of points must be altered to drive the value of an Estimator to infinity. But despite this, many of them can be inordinately influenced by two properly placed outliers. With one predictor, an Estimator that appears to correct this problem to a fair degree, and simultaneously maintain good efficiency when standard assumptions are met, consists of checking for outliers using a projection-type method, removing any that are found, and applying the Theil-Sen Estimator to the data that remain. When dealing with multiple predictors, there are two generalizations of the Theil-Sen Estimator that might be used, but nothing is known about how their small-sample properties compare. Also, there are no results on testing the hypothesis of zero slopes, and there is no information about the effect on efficiency when outliers are removed. In terms of hypothesis testing, using the more obvious percentile bootstrap method in conjunction with a slight modification of Mahalanobis distance was found to avoid Type I error probabilities above the nominal level, but in some situations the actual Type I error probabilities can be substantially smaller than intended when the sample size is small. An alternative method is found to be more satisfactory.
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simulations on the theil Sen regression Estimator with right censored data
Statistics & Probability Letters, 1998Co-Authors: Rand R. WilcoxAbstract:This note compares the small-sample efficiency of the extended Theil-Sen Estimator to the modified Buckley-James Estimator when the predictor is random. Included are situations where the error term is heteroscedastic. In terms of their standard errors, the extended Theil-Sen Estimator is found to offer a substantial advantage in various situations, while the modified Buckley-James Estimator never offers an advantage when there is 20% or 50% censoring.
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a note on the theil Sen regression Estimator when the regressor is random and the error term is heteroscedastic
Biometrical Journal, 1998Co-Authors: Rand R. WilcoxAbstract:In simple regression, two serious problems with the ordinary least squares (OLS) Estimator are that its efficiency can be relatively poor when the error term is normal but heteroscedastic, and the usual confidence interval for the slope can have highly unsatisfactory probability coverage. When the error term is nonnormal, these problems become exacerbated. Two other concerns are that the OLS Estimator has an unbounded influence function and a breakdown point of zero. Wilcox (1996) compared several Estimators when there is heteroscedasticity and found two that have relatively good efficiency and simultaneously provide protection against outliers: an M-Estimator with Schweppe weights and an Estimator proposed by Cohen, Dalal and Tukey (1993). However, the M-Estimator can handle only one outlier in the X-domain or among the Y values, and among the methods considered by Wilcox for computing confidence intervals for the slope, none performed well when working with the Cohen-Dalal-Tukey Estimator. This note points out that the small-sample efficiency of theTheil-Sen Estimator competes well with the Estimators considered by Wilcox, and a method for computing a confidence interval was found that performs well in simulations. The Theil-Sen Estimator has a reasonably high breakdown point, a bounded influence function, and in some cases its small-sample efficiency offers a substantial advantage over all of the Estimators compared in Wilcox (1996).
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simulation results on extensions of the theil Sen regression Estimator
Communications in Statistics - Simulation and Computation, 1998Co-Authors: Rand R. WilcoxAbstract:The efficiency of the the ordinary least squares (OLS) regression Estimator can be very poor when the error term is normal but heteroscedastic. When the error term is nonnormal, the problem is exacerbated. Several Estimators have been found to have high small-sample efficiency cmpared to the OLS Estimator when the error term is heteroscedastic, and little efficiency is lost when in fact the error term is normal and homoscedastic. One of these is the Theil-Sen Estimator with one regressor. The goal in this paper is to consider four extensions of this Estimator to two regressors, one of which is found to have practical advantages over the other three. Moreover, its small-sample efficiency is found to be considerable compared to the OLS Estimator, and the number of elemental subsets required to compute it isequal to the number of elemental subsets required when there is onlyone predictor.
Michael P Lavalley - One of the best experts on this subject based on the ideXlab platform.
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the theil Sen Estimator with doubly censored data and applications to astronomy
Journal of the American Statistical Association, 1995Co-Authors: Michael G Akritas, Susan A Murphy, Michael P LavalleyAbstract:Abstract The Theil-Sen Estimator of the slope parameter in simple linear regression is extended to data with both the response and the covariate subject to censoring. Based on inverting a suitable version of Kendall's τ statistic, this Estimator requires weak assumptions and is simple to compute, and a simple estimate of its asymptotic variance is obtained. A second extension of the Theil-Sen Estimator, based on a direct estimation of the median of pairwise slopes, is given. These Estimators are compared numerically with versions of Schmitt's Estimator and applied to two data sets from the recent astronomical literature.
Xueqin Wang - One of the best experts on this subject based on the ideXlab platform.
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consistency and asymptotic distribution of the theil Sen Estimator
Journal of Statistical Planning and Inference, 2008Co-Authors: Hanxiang Peng, Xueqin Wang, Shaoli WangAbstract:Abstract In this paper, we obtain the strong consistency and asymptotic distribution of the Theil–Sen Estimator in simple linear regression models with arbitrary error distributions. We show that the Theil–Sen Estimator is super-efficient when the error distribution is discontinuous and that its asymptotic distribution may or may not be normal when the error distribution is continuous. We give an example in which the Theil–Sen Estimator is not asymptotically normal. A small simulation study is conducted to confirm the super-efficiency and the non-normality of the asymptotic distribution.
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unbiasedness of the theil Sen Estimator
Journal of Nonparametric Statistics, 2005Co-Authors: Xueqin WangAbstract:We consider the simple linear regression model. The Theil–Sen Estimator is a point Estimator of the slope parameter in the model and has many nice properties, most of which are established by Sen. Thus, it is introduced in several classical textbooks on non-parametric statistics. Sen also gave a proof that the Theil–Sen Estimator is unbiased under the assumption that the error distribution is continuous. The statement is incorrect. We construct several counterexamples. Furthermore, we show that the continuity assumption on the error distribution is not important to unbiasedness. In particular, if the sample size n = 2 or 3, then the Theil–Sen Estimator is unbiased. Moreover, if either the error distribution or the covariates have certain symmetry, then the Theil–Sen Estimator is also unbiased.
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asymptotics of the theil Sen Estimator in the simple linear regression model with a random covariate
Journal of Nonparametric Statistics, 2005Co-Authors: Xueqin WangAbstract:We consider a simple linear regression model. The Theil–Sen Estimator (TSE) is a point Estimator of the slope parameter in the model and has many nice properties, including asymptotic normality. Thus, it has been introduced in several classical textbooks on non-parametric statistics. Most of its properties are established under the assumptions that the error distribution is absolutely continuous and the covariate is not random. In this paper, we study asymptotic properties of the TSE in a simple linear regression model with a random covariate and an arbitrary error distribution, which may not be continuous. We show that it is strongly consistent and has an asymptotic distribution, which may not be a normal distribution if the error distribution is not absolutely continuous.
Michael G Akritas - One of the best experts on this subject based on the ideXlab platform.
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the theil Sen Estimator with doubly censored data and applications to astronomy
Journal of the American Statistical Association, 1995Co-Authors: Michael G Akritas, Susan A Murphy, Michael P LavalleyAbstract:Abstract The Theil-Sen Estimator of the slope parameter in simple linear regression is extended to data with both the response and the covariate subject to censoring. Based on inverting a suitable version of Kendall's τ statistic, this Estimator requires weak assumptions and is simple to compute, and a simple estimate of its asymptotic variance is obtained. A second extension of the Theil-Sen Estimator, based on a direct estimation of the median of pairwise slopes, is given. These Estimators are compared numerically with versions of Schmitt's Estimator and applied to two data sets from the recent astronomical literature.
Ierley Glenn - One of the best experts on this subject based on the ideXlab platform.
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A universal rank-order transform to extract signals from noisy data
'American Physical Society (APS)', 2019Co-Authors: Ierley Glenn, Kostinski AlexAbstract:We introduce an ordinate method for noisy data analysis, based solely on rank information and thus inSensitive to outliers. The method is nonparametric, objective, and the required data processing is parsimonious. Main ingredients are a rank-order data matrix and its transform to a stable form, which provide linear trends in excellent agreement with least squares regression, despite the loss of magnitude information. A group symmetry orthogonal decomposition of the 2D rank-order transform for iid (white) noise is further ordered by principal component analysis. This two-step procedure provides a noise "etalon" used to characterize arbitrary stationary stochastic processes. The method readily distinguishes both the Ornstein-Uhlenbeck process and chaos generated by the logistic map from white noise. Ranking within randomness differs fundamentally from that in deterministic chaos and signals, thus forming the basis for signal detection. To further illustrate the breadth of applications, we apply this ordinate method to the canonical nonlinear parameter estimation problem of two-species radioactive decay, outperforming special-purpose least square software. It is demonstrated that the method excels when extracting trends in heavy-tailed noise and, unlike the Thiele-Sen Estimator, is not limited to linear regression. Lastly, a simple expression is given that yields a close approximation for signal extraction of an underlying generally nonlinear signal.Comment: 26 pages, 18 figure
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Universal rank-order transform to extract signals from noisy data
Digital Commons @ Michigan Tech, 2019Co-Authors: Ierley Glenn, Kostinski AlexanderAbstract:We introduce an ordinate method for noisy data analysis, based solely on rank information and thus inSensitive to outliers. The method is nonparametric and objective, and the required data processing is parsimonious. The main ingredients include a rank-order data matrix and its transform to a stable form, which provide linear trends in excellent agreement with least squares regression, despite the loss of magnitude information. A group symmetry orthogonal decomposition of the 2D rank-order transform for iid (white) noise is further ordered by principal component analysis. This two-step procedure provides a noise “etalon” used to characterize arbitrary stationary stochastic processes. The method readily distinguishes both the Ornstein-Uhlenbeck process and chaos generated by the logistic map from white noise. Ranking within randomness differs fundamentally from that in deterministic chaos and signals, thus forming the basis for signal detection. To further illustrate the breadth of applications, we apply this ordinate method to the canonical nonlinear parameter estimation problem of two-species radioactive decay, outperforming special-purpose least squares software. We demonstrate that the method excels when extracting trends in heavy-tailed noise and, unlike the Thiele-Sen Estimator, is not limited to linear regression. A simple expression is given that yields a close approximation for signal extraction of an underlying, generally nonlinear signal
