手法を比較

	MM推定によるロバスト回帰	ロバスト回帰のためのS推定量	Theil-Sen推定量
分野	統計学	統計学	統計学
系統	Regression model	Regression model	Regression model
提唱年	1987	1984	1968
提唱者	Victor J. Yohai	Rousseeuw & Yohai (1984)	Henri Theil (1950); P. K. Sen (1968)
種類	Robust linear regression	Robust linear regression	Robust linear regression
原典	Yohai, V. J. (1987). High Breakdown-Point and High Efficiency Robust Estimates for Regression. Annals of Statistics, 15(2), 642-656.	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.
別名	MM-estimation, MM robust regression, high-breakdown high-efficiency estimator, MM-Tahmin Edici	S-estimation, robust S-regression, S-Tahmin Edici	Theil-Sen Tahmincisi, Theil-Sen regression, median slope estimator, Sen's slope estimator
関連	5	5	6
概要	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.	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%.