手法を比較

	M推定量（ロバスト回帰）	Least Trimmed Squares (LTS) 回帰分析	分位点回帰
分野	統計学	統計学	計量経済学
系統	Regression model	Regression model	Regression model
提唱年	2009	1984	1978
提唱者	Peter J. Huber	Peter J. Rousseeuw	Koenker & Bassett
種類	Robust linear regression	Robust linear regression	Conditional quantile regression
原典	Huber, P. J., & Ronchetti, E. M. (2009). Robust Statistics (2nd ed.). Wiley.	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.
別名	m-estimation, huber regression, robust m-regression, M-Tahmin Ediciler	LTS, least trimmed squares regression, trimmed least squares, robust regression	conditional quantile regression, regression quantiles, Kantil Regresyon
関連	5	5	5
概要	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.	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.