مقایسهٔ روش‌ها

	برآوردگر MM برای رگرسیون استوار	رگرسیون حداقل مربعات معمولی (OLS)	رگرسیون کوانتایل	تخمین‌گر تاو (τ) رگرسیون
حوزه	آمار	اقتصادسنجی	اقتصادسنجی	آمار
خانواده	Regression model	Regression model	Regression model	Regression model
سال پیدایش	1987	2019	1978	1988
پدیدآور	Victor J. Yohai	Wooldridge (textbook treatment); classical least squares	Koenker & Bassett	Yohai & Zamar
نوع	Robust linear regression	Linear regression	Conditional quantile regression	Robust linear regression
منبع بنیادین	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	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.
نام‌های دیگر	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	conditional quantile regression, regression quantiles, Kantil Regresyon	tau regression estimator, robust tau regression, Tau-Tahmin Edici
مرتبط	5	5	5	4
خلاصه	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).	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.