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	डब्ल्यू-एस्टिमेटर रोबस्ट रिग्रेशन (वेल्श / टुकी बिस्क्वेयर)	साधारण न्यूनतम वर्ग (OLS) समाश्रयण	एस-अनुमानक (S-Estimator) सुदृढ़ प्रतिगमन (Robust Regression) के लिए	थेल-सेन अनुमानक
क्षेत्र	सांख्यिकी	अर्थमिति	सांख्यिकी	सांख्यिकी
परिवार	Regression model	Regression model	Regression model	Regression model
उद्भव वर्ष	1974	2019	1984	1968
प्रवर्तक	Beaton & Tukey (bisquare weight); Welsch (Welsch weight)	Wooldridge (textbook treatment); classical least squares	Rousseeuw & Yohai (1984)	Henri Theil (1950); P. K. Sen (1968)
प्रकार	Robust regression (redescending M-estimator)	Linear regression	Robust linear regression	Robust linear regression
मौलिक स्रोत	Beaton, A. E. & Tukey, J. W. (1974). The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data. Technometrics, 16(2), 147-185.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860	Rousseeuw, P. J. & Yohai, V. J. (1984). Robust Regression by Means of S-Estimators. In Robust and Nonlinear Time Series Analysis (Lecture Notes in Statistics, Vol. 26, pp. 256-272). Springer.	Sen, P. K. (1968). Estimates of the Regression Coefficient Based on Kendall's Tau. Journal of the American Statistical Association, 63(324), 1379-1389.
उपनाम	Tukey bisquare M-estimator, Welsch M-estimator, redescending M-estimator, W-Tahmin Edici (Welsch / Tukey Bisquare)	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	S-estimation, robust S-regression, S-Tahmin Edici	Theil-Sen Tahmincisi, Theil-Sen regression, median slope estimator, Sen's slope estimator
संबंधित	4	5	5	6
सारांश	The W-estimator is a family of robust M-estimator variants for linear regression that use the Tukey bisquare and Welsch weight functions, introduced in the line of work going back to Beaton and Tukey (1974). Because its weights fall rapidly toward zero as a residual grows, it resists outliers more strongly than the Huber M-estimator.	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).	The S-estimator is a robust linear-regression method, introduced by Rousseeuw and Yohai in 1984, that estimates the coefficients by minimising a robust M-estimate of the residual scale rather than the variance of the residuals. By driving down a bounded measure of residual spread it can attain a breakdown point of up to 50%, so it stays reliable even when a large share of the data are outliers, and it provides the first stage of the well-known MM-estimator.	The Theil-Sen estimator is a robust linear regression method that estimates the slope as the median of the slopes computed over all pairs of data points. Introduced by Henri Theil in 1950 and extended by P. K. Sen in 1968, it tolerates outliers in the response with a breakdown point of about 29%.