Estimates of the Regression Coefficient Based on Kendall's Tau

By Pranab Kumar Sen. 1968

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Surrogate-Assisted Evolutionary Deep Learning Using an End-to-End Random Forest-Based Performance Predictor (2020, methodology): “For the quantitative comparison, we choose the mean square error (MSE), Kendall’s Tau (KTau) [64], and the coefficient of determination (CoD) [65] as the indicators suggested in [32].”
Identification of Trend in Reference Evapotranspiration Series with Serial Dependence in Iran (2012, methodology): “…EðXtÞ½ Xtþ1 EðXtÞ½ 1 n Pn t¼1 Xt EðXtÞ½ 2 ð11aÞ EðXtÞ ¼ 1n Xn t¼1 Xt ð11bÞ Theil–Sen’s Estimator The magnitude of the trends in the ETo time series was estimated using the non-parametric Theil–Sen’s estimator (Theil 1950; Sen 1968) as follows: b ¼ Median Xi Xj i j ; 8j < i ð12Þ in which 1< j< i<n.”
Rating curve estimation under epistemic uncertainty (2015, methodology): “Robust statistical methods, such as the Theil–Sen estimator for robust linear regression in the presence of outliers, rely on sampling all pairs of points to calculate regression slope (Sen, 1968).”
Consistency and asymptotic distribution of the Theil–Sen estimator (2008, methodology): “A well-known robust estimator of the slope β is the Theil-Sen estimator that was first proposed by Theil (1950) and then extended by Sen (1968).”
Linear valuation without OLS: the Theil-Sen estimation approach (2014, unknown): “This paper applies the so-called Theil–Sen (TS) method (Theil 1950; Sen 1968) to estimate linear models.”
Robustness in Data Analysis: Criteria and Methods (2001, background): “The LMS, LTS, and other regressions Various robust estimators have been proposed to provide high global robustness of estimation, among them the median of pairwise slopes (Theil, 1950; Adichie, 1967; Sen, 1968); the resistant line (Tukey, 1977; Velleman and Hoaglin, 1981); L-estimators (Bickel, 1973”
Assessment of drought trend and variability in India using wavelet transform (2020, methodology): “2 Sen’s slope estimator The magnitude of the trend in a time series is determined using the non-parametric method, Sen’s estimator of slope (Sen 1968).”
A comparison of the power of the t test, Mann-Kendall and bootstrap tests for trend detection / Une comparaison de la puissance des tests t de Student, de Mann-Kendall et du bootstrap pour la détection de tendance (2004, methodology): “Suppose that an observed sample data set, X (= x1, x2, ..., xn) is available, from which the magnitude of trend, bo, of interest can be computed using the approach by Theil (1950) and Sen (1968) , hereafter referred to as the Theil-Sen Approach (TSA).”
Permutation inference for the general linear model (2014, methodology): “Statistics that can be used include, for instance, those based on ranks of observations (Brunner and Munzel, 2000; Rorden et al., 2007), derived from regression methods other than least squares (Cade and Richards, 1996) or that are robust to outliers (Sen, 1968; Theil, 1950).”