手法を比較

	M推定量（ロバスト回帰）	最小二乗法 (OLS) 回帰	分位点回帰
分野	統計学	計量経済学	計量経済学
系統	Regression model	Regression model	Regression model
提唱年	2009	2019	1978
提唱者	Peter J. Huber	Wooldridge (textbook treatment); classical least squares	Koenker & Bassett
種類	Robust linear regression	Linear regression	Conditional quantile regression
原典	Huber, P. J., & Ronchetti, E. M. (2009). Robust Statistics (2nd ed.). Wiley.	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.
別名	m-estimation, huber regression, robust m-regression, M-Tahmin Ediciler	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	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.	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.