مقایسهٔ روش‌ها

	رگرسیون هیوبر	تخمین‌گرهای M (رگرسیون مقاوم)	برآوردگر MM برای رگرسیون استوار	رگرسیون حداقل مربعات معمولی (OLS)
حوزه	آمار	آمار	آمار	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model	Regression model
سال پیدایش	1964	2009	1987	2019
پدیدآور	Peter J. Huber	Peter J. Huber	Victor J. Yohai	Wooldridge (textbook treatment); classical least squares
نوع	Robust linear regression (M-estimation)	Robust linear regression	Robust linear regression	Linear regression
منبع بنیادین	Huber, P. J. (1964). Robust Estimation of a Location Parameter. Annals of Mathematical Statistics, 35(1), 73-101.	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.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860
نام‌های دیگر	Huber M-estimator, Huber loss regression, robust regression, Huber Regresyonu	m-estimation, huber regression, robust m-regression, M-Tahmin Ediciler	MM-estimation, MM robust regression, high-breakdown high-efficiency estimator, MM-Tahmin Edici	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu
مرتبط	5	5	5	5
خلاصه	Huber regression is a robust linear regression method, introduced by Peter J. Huber in 1964, that resists the influence of outliers by treating small and large residuals differently. It applies a squared (OLS-like) loss to small residuals and a milder absolute-value loss to large ones, so extreme observations cannot dominate the fit.	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.	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).