Vertaile menetelmiä

	Robust Regression	Vähiten katkaistujen neliöiden (LTS) regressio	OLS-regressio (Ordinary Least Squares)	Kvanttiiliregressio
Tieteenala	Tilastotiede	Tilastotiede	Ekonometria	Ekonometria
Menetelmäperhe	Regression model	Regression model	Regression model	Regression model
Syntyvuosi	1964	1984	2019	1978
Kehittäjä	Peter J. Huber (M-estimation, 1964); Frank Hampel (influence function, 1974)	Peter J. Rousseeuw	Wooldridge (textbook treatment); classical least squares	Koenker & Bassett
Tyyppi	Regression with outlier resistance	Robust linear regression	Linear regression	Conditional quantile regression
Alkuperäislähde	Huber, P. J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), 73–101.	Rousseeuw, P. J. (1984). Least Median of Squares Regression. Journal of the American Statistical Association, 79(388), 871-880.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860	Koenker, R. & Bassett, G., Jr. (1978). Regression Quantiles. Econometrica, 46(1), 33-50.
Rinnakkaisnimet	M-estimation regression, robust linear regression, outlier-resistant regression, MM-estimation	LTS, least trimmed squares regression, trimmed least squares, robust regression	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	conditional quantile regression, regression quantiles, Kantil Regresyon
Liittyvät	6	5	5	5
Tiivistelmä	Robust regression estimates the linear relationship between a continuous outcome and predictors while sharply reducing the influence of outliers and leverage points. Unlike OLS, which is highly sensitive to extreme observations, robust methods assign down-weighted influence to atypical data points, producing coefficient estimates that remain stable even when a fraction of the data is contaminated or non-normally distributed.	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.	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).	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.