পদ্ধতির তুলনা করুন

	এস-অনুমানক (S-Estimator) রোবাস্ট রিগ্রেশনের জন্য	MM-Estimation for Robust Regression	সাধারণ ন্যূনতম বর্গক্ষেত্র (OLS) রিগ্রেশন	কোয়ান্টাইল রিগ্রেশন	রিগ্রেশনের টাউ (τ) প্রাক্কলক
ক্ষেত্র	পরিসংখ্যান	পরিসংখ্যান	অর্থমিতি	অর্থমিতি	পরিসংখ্যান
পরিবার	Regression model	Regression model	Regression model	Regression model	Regression model
উদ্ভবের বছর	1984	1987	2019	1978	1988
প্রবর্তক	Rousseeuw & Yohai (1984)	Victor J. Yohai	Wooldridge (textbook treatment); classical least squares	Koenker & Bassett	Yohai & Zamar
ধরন	Robust linear regression	Robust linear regression	Linear regression	Conditional quantile regression	Robust linear regression
মৌলিক উৎস	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.	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.
অপর নাম	S-estimation, robust S-regression, S-Tahmin Edici	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
সম্পর্কিত	5	5	5	5	4
সারসংক্ষেপ	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.	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.