Сравнение на методи

	S-оценка за робастна регресия	Квантилна регресия	Оценъчен метод Тау (τ) за регресия
Област	Статистика	Иконометрия	Статистика
Семейство	Regression model	Regression model	Regression model
Година на възникване	1984	1978	1988
Създател	Rousseeuw & Yohai (1984)	Koenker & Bassett	Yohai & Zamar
Тип	Robust linear regression	Conditional quantile regression	Robust linear regression
Основополагащ източник	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.	Koenker, R. & Bassett, G., Jr. (1978). Regression Quantiles. Econometrica, 46(1), 33-50.	Yohai, V. J., & Zamar, R. H. (1988). High Breakdown-Point Estimates of Regression by Means of the Minimization of an Efficient Scale. Journal of the American Statistical Association, 83(402), 406-413.
Други названия	S-estimation, robust S-regression, S-Tahmin Edici	conditional quantile regression, regression quantiles, Kantil Regresyon	tau regression estimator, robust tau regression, Tau-Tahmin Edici
Свързани	5	5	4
Резюме	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.	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.	The Tau estimator is a robust linear regression method introduced by Yohai and Zamar in 1988 that fits the model by minimising an efficient τ-scale of the residuals. It builds on the scale estimate of the S-estimator to combine a high breakdown point with high statistical efficiency, and is often used as an alternative to the MM-estimator in small samples.