เปรียบเทียบวิธี

	การถดถอยแบบแข็งแกร่งด้วย W-Estimator (Welsch / Tukey Bisquare)	การประมาณค่า MM สำหรับการถดถอยที่แข็งแกร่ง (Robust Regression)	การถดถอยกำลังสองน้อยที่สุดสามัญ (OLS)
สาขาวิชา	สถิติศาสตร์	สถิติศาสตร์	เศรษฐมิติ
ตระกูล	Regression model	Regression model	Regression model
ปีกำเนิด	1974	1987	2019
ผู้ริเริ่ม	Beaton & Tukey (bisquare weight); Welsch (Welsch weight)	Victor J. Yohai	Wooldridge (textbook treatment); classical least squares
ประเภท	Robust regression (redescending M-estimator)	Robust linear regression	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.	Yohai, V. J. (1987). High Breakdown-Point and High Efficiency Robust Estimates for Regression. Annals of Statistics, 15(2), 642-656.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860
ชื่อเรียกอื่น	Tukey bisquare M-estimator, Welsch M-estimator, redescending M-estimator, W-Tahmin Edici (Welsch / Tukey Bisquare)	MM-estimation, MM robust regression, high-breakdown high-efficiency estimator, MM-Tahmin Edici	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu
ที่เกี่ยวข้อง	4	5	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 MM-estimator is a robust linear regression method introduced by Victor J. Yohai in 1987. It combines the high breakdown point of an S-estimator with the high efficiency of an M-estimator, so it resists outliers strongly while still using the data efficiently when errors are well-behaved.	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).