手法を比較

	頑健回帰	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	1964	1984	1978
提唱者	Peter J. Huber (M-estimation, 1964); Frank Hampel (influence function, 1974)	Peter J. Rousseeuw	Koenker & Bassett
種類	Regression with outlier resistance	Robust linear regression	Conditional quantile regression
原典	Huber, P. J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), 73–101.	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 regression, robust linear regression, outlier-resistant regression, MM-estimation	LTS, least trimmed squares regression, trimmed least squares, robust regression	conditional quantile regression, regression quantiles, Kantil Regresyon
関連	6	5	5
概要	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.	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.