手法を比較

	影響診断（Cook距離、DFFITS、レバレッジ）	中央絶対偏差 (MAD) 推定	最小二乗法 (OLS) 回帰	分位点回帰
分野	統計学	統計学	計量経済学	計量経済学
系統	Regression model	Regression model	Regression model	Regression model
提唱年	1977	1974	2019	1978
提唱者	R. Dennis Cook (Cook's distance); Belsley, Kuh & Welsch (DFFITS, leverage)	Hampel (influence-curve treatment); classical robust statistics	Wooldridge (textbook treatment); classical least squares	Koenker & Bassett
種類	Regression diagnostic	Robust scale estimator	Linear regression	Conditional quantile regression
原典	Cook, R. D. (1977). Detection of Influential Observations in Linear Regression. Technometrics, 19(1), 15-18.	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.
別名	Cook's distance, DFFITS, leverage, influential observation detection	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
関連	5	5	5	5
概要	Influence diagnostics are a family of post-fit measures that quantify how much each single observation affects a fitted regression. Cook's distance was introduced by R. Dennis Cook in 1977, with leverage and DFFITS formalised by Belsley, Kuh and Welsch in 1980, to flag the observations that most strongly pull the estimated coefficients.	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.