方法对比

	M估计量（稳健回归）	MM估计量稳健回归	分位数回归
领域	统计学	统计学	计量经济学
方法族	Regression model	Regression model	Regression model
起源年份	2009	1987	1978
提出者	Peter J. Huber	Victor J. Yohai	Koenker & Bassett
类型	Robust linear regression	Robust linear regression	Conditional quantile regression
开创性文献	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.
别名	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
相关	5	5	5
摘要	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.