เปรียบเทียบวิธี

	การถดถอยแบบแข็งแกร่งด้วย W-Estimator (Welsch / Tukey Bisquare)	S-Estimator สำหรับการถดถอยที่ทนทาน
สาขาวิชา	สถิติศาสตร์	สถิติศาสตร์
ตระกูล	Regression model	Regression model
ปีกำเนิด	1974	1984
ผู้ริเริ่ม	Beaton & Tukey (bisquare weight); Welsch (Welsch weight)	Rousseeuw & Yohai (1984)
ประเภท	Robust regression (redescending M-estimator)	Robust linear regression
แหล่งต้นตำรับ	Beaton, A. E. & Tukey, J. W. (1974). The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data. Technometrics, 16(2), 147-185.	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.
ชื่อเรียกอื่น	Tukey bisquare M-estimator, Welsch M-estimator, redescending M-estimator, W-Tahmin Edici (Welsch / Tukey Bisquare)	S-estimation, robust S-regression, S-Tahmin Edici
ที่เกี่ยวข้อง	4	5
สรุป	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.	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.