手法を比較

	中央絶対偏差 (MAD) 推定	最小二乗法 (OLS) 回帰	分位点回帰	リッジ回帰
分野	統計学	計量経済学	計量経済学	機械学習
系統	Regression model	Regression model	Regression model	Machine learning
提唱年	1974	2019	1978	1970
提唱者	Hampel (influence-curve treatment); classical robust statistics	Wooldridge (textbook treatment); classical least squares	Koenker & Bassett	Hoerl, A.E. & Kennard, R.W.
種類	Robust scale estimator	Linear regression	Conditional quantile regression	L2-regularized linear regression
原典	Hampel, F. R. (1974). The Influence Curve and Its Role in Robust Estimation. Journal of the American Statistical Association, 69(346), 383-393.	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.	Hoerl, A.E. & Kennard, R.W. (1970). Ridge Regression: Biased Estimation for Nonorthogonal Problems. Technometrics, 12(1), 55–67.
別名	median absolute deviation, MAD scale estimator, robust scale estimation, Medyan Mutlak Sapma (MAD) Tahmini	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	conditional quantile regression, regression quantiles, Kantil Regresyon	Ridge Regresyonu, ridge regresyonu, L2-regularized regression, Tikhonov regularization
関連	5	5	5	4
概要	Median Absolute Deviation estimation is a robust measure of statistical dispersion that replaces the standard deviation when outliers are present. Rooted in the influence-curve framework formalised by Hampel (1974), it summarises the spread of a continuous variable using medians instead of means, so a single extreme value cannot distort the result.	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.	Ridge Regression is an L2-regularized linear regression method, introduced by Arthur Hoerl and Robert Kennard in 1970, that reduces multicollinearity by adding a penalty on the size of the coefficients. It shrinks coefficients toward zero without setting any of them exactly to zero, producing more stable estimates when predictors are highly correlated.