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	एमएम-अनुमान (MM-Estimation) सघन प्रतिगमन (Robust Regression) के लिए	साधारण न्यूनतम वर्ग (OLS) समाश्रयण	क्वांटाइल रिग्रेशन	रिग्रेशन का टाऊ (τ) अनुमानक
क्षेत्र	सांख्यिकी	अर्थमिति	अर्थमिति	सांख्यिकी
परिवार	Regression model	Regression model	Regression model	Regression model
उद्भव वर्ष	1987	2019	1978	1988
प्रवर्तक	Victor J. Yohai	Wooldridge (textbook treatment); classical least squares	Koenker & Bassett	Yohai & Zamar
प्रकार	Robust linear regression	Linear regression	Conditional quantile regression	Robust linear regression
मौलिक स्रोत	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.
उपनाम	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
संबंधित	5	5	5	4
सारांश	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.