Vertaile menetelmiä

	M-estimaattorit (Robustin regressio)	Vähiten katkaistujen neliöiden (LTS) regressio	MM-estimaattori vankalle regressiolle
Tieteenala	Tilastotiede	Tilastotiede	Tilastotiede
Menetelmäperhe	Regression model	Regression model	Regression model
Syntyvuosi	2009	1984	1987
Kehittäjä	Peter J. Huber	Peter J. Rousseeuw	Victor J. Yohai
Tyyppi	Robust linear regression	Robust linear regression	Robust linear regression
Alkuperäislähde	Huber, P. J., & Ronchetti, E. M. (2009). Robust Statistics (2nd ed.). Wiley.	Rousseeuw, P. J. (1984). Least Median of Squares Regression. Journal of the American Statistical Association, 79(388), 871-880.	Yohai, V. J. (1987). High Breakdown-Point and High Efficiency Robust Estimates for Regression. Annals of Statistics, 15(2), 642-656.
Rinnakkaisnimet	m-estimation, huber regression, robust m-regression, M-Tahmin Ediciler	LTS, least trimmed squares regression, trimmed least squares, robust regression	MM-estimation, MM robust regression, high-breakdown high-efficiency estimator, MM-Tahmin Edici
Liittyvät	5	5	5
Tiivistelmä	M-estimators are a robust generalisation of maximum likelihood estimation, formalised in the work of Peter J. Huber (Huber & Ronchetti, 2009). Instead of squaring every residual, they apply a bounded loss function so that large residuals from outliers are down-weighted rather than allowed to dominate the fit.	Least Trimmed Squares is a robust linear regression method introduced by Peter J. Rousseeuw in 1984. Instead of fitting all residuals, it estimates the coefficients by minimising the sum of only the h smallest squared residuals, which gives it a breakdown point of up to 50% and reliable estimates on data heavily contaminated by outliers.	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.