방법 비교

	W-추정량 로버스트 회귀 (Welsch / Tukey Bisquare)	MM-추정량을 이용한 강건 회귀분석	최소제곱법(OLS) 회귀	S-Estimator
분야	통계학	통계학	계량경제학	통계학
계열	Regression model	Regression model	Regression model	Regression model
기원 연도	1974	1987	2019	1984
창시자	Beaton & Tukey (bisquare weight); Welsch (Welsch weight)	Victor J. Yohai	Wooldridge (textbook treatment); classical least squares	Rousseeuw & Yohai (1984)
유형	Robust regression (redescending M-estimator)	Robust linear regression	Linear regression	Robust linear regression
원전	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	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.
별칭	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	S-estimation, robust S-regression, S-Tahmin Edici
관련	4	5	5	5
요약	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).	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.