方法对比

	稳健回归	Lasso 回归	最小裁剪平方和（LTS）回归	分位数回归
领域	统计学	机器学习	统计学	计量经济学
方法族	Regression model	Machine learning	Regression model	Regression model
起源年份	1964	1996	1984	1978
提出者	Peter J. Huber (M-estimation, 1964); Frank Hampel (influence function, 1974)	Tibshirani, R.	Peter J. Rousseeuw	Koenker & Bassett
类型	Regression with outlier resistance	Regularized linear regression (L1 penalty)	Robust linear regression	Conditional quantile regression
开创性文献	Huber, P. J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), 73–101.	Tibshirani, R. (1996). Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society: Series B, 58(1), 267–288.	Rousseeuw, P. J. (1984). Least Median of Squares Regression. Journal of the American Statistical Association, 79(388), 871-880.	Koenker, R. & Bassett, G., Jr. (1978). Regression Quantiles. Econometrica, 46(1), 33-50.
别名	M-estimation regression, robust linear regression, outlier-resistant regression, MM-estimation	LASSO Regresyonu, lasso, L1-regularized regression, L1 regularization	LTS, least trimmed squares regression, trimmed least squares, robust regression	conditional quantile regression, regression quantiles, Kantil Regresyon
相关	6	4	5	5
摘要	Robust regression estimates the linear relationship between a continuous outcome and predictors while sharply reducing the influence of outliers and leverage points. Unlike OLS, which is highly sensitive to extreme observations, robust methods assign down-weighted influence to atypical data points, producing coefficient estimates that remain stable even when a fraction of the data is contaminated or non-normally distributed.	Lasso regression, introduced by Robert Tibshirani in 1996, is a linear regression method that adds an L1 penalty to the loss so that it shrinks coefficients and performs variable selection at the same time, producing a sparse model. By driving some coefficients exactly to zero it keeps only the predictors that matter.	Least Trimmed Squares is a robust linear regression method introduced by Peter J. Rousseeuw in 1984. Instead of fitting all residuals, it estimates the coefficients by minimising the sum of only the h smallest squared residuals, which gives it a breakdown point of up to 50% and reliable estimates on data heavily contaminated by outliers.	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.