مقایسهٔ روش‌ها

	تخمین‌گرهای M (رگرسیون مقاوم)	برآوردگر MM برای رگرسیون استوار	رگرسیون کوانتایل
حوزه	آمار	آمار	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model
سال پیدایش	2009	1987	1978
پدیدآور	Peter J. Huber	Victor J. Yohai	Koenker & Bassett
نوع	Robust linear regression	Robust linear regression	Conditional quantile regression
منبع بنیادین	Huber, P. J., & Ronchetti, E. M. (2009). Robust Statistics (2nd ed.). Wiley.	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.
نام‌های دیگر	m-estimation, huber regression, robust m-regression, M-Tahmin Ediciler	MM-estimation, MM robust regression, high-breakdown high-efficiency estimator, MM-Tahmin Edici	conditional quantile regression, regression quantiles, Kantil Regresyon
مرتبط	5	5	5
خلاصه	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.	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.