So sánh phương pháp

	Ước lượng S cho hồi quy vững mạnh	Ước lượng MM cho hồi quy vững mạnh	Hồi quy Quantile
Lĩnh vực	Thống kê	Thống kê	Kinh tế lượng
Họ	Regression model	Regression model	Regression model
Năm ra đời	1984	1987	1978
Người khởi xướng	Rousseeuw & Yohai (1984)	Victor J. Yohai	Koenker & Bassett
Loại	Robust linear regression	Robust linear regression	Conditional quantile regression
Công trình gốc	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.	Yohai, V. J. (1987). High Breakdown-Point and High Efficiency Robust Estimates for Regression. Annals of Statistics, 15(2), 642-656.	Koenker, R. & Bassett, G., Jr. (1978). Regression Quantiles. Econometrica, 46(1), 33-50.
Tên gọi khác	S-estimation, robust S-regression, S-Tahmin Edici	MM-estimation, MM robust regression, high-breakdown high-efficiency estimator, MM-Tahmin Edici	conditional quantile regression, regression quantiles, Kantil Regresyon
Liên quan	5	5	5
Tóm tắt	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 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.	Quantile regression models conditional quantiles of an outcome - the median, the 25th or 75th percentile, and so on - rather than the conditional mean that OLS targets. Introduced by Koenker and Bassett in 1978, it reveals how predictors act across the whole distribution, including its tails.