手法を比較

	ロバスト・マハラノビス距離	中央絶対偏差 (MAD) 推定	ロバストANOVA（ウェルチとトリム平均）
分野	統計学	統計学	統計学
系統	Regression model	Regression model	Regression model
提唱年	1990	1974	1951
提唱者	Rousseeuw & Van Zomeren (robust distance); Filzmoser, Garrett & Reimann (multivariate outlier detection)	Hampel (influence-curve treatment); classical robust statistics	Welch (1951); robust trimmed-mean approach popularised by Wilcox
種類	Robust multivariate outlier detection	Robust scale estimator	Robust one-way analysis of variance
原典	Rousseeuw, P. J. & Van Zomeren, B. C. (1990). Unmasking Multivariate Outliers and Leverage Points. Journal of the American Statistical Association, 85(411), 633-639.	Hampel, F. R. (1974). The Influence Curve and Its Role in Robust Estimation. Journal of the American Statistical Association, 69(346), 383-393.	Welch, B. L. (1951). On the comparison of several mean values: an alternative approach. Biometrika, 38(3/4), 330-336.
別名	MCD Mahalanobis distance, robust mahalanobis, minimum covariance determinant distance, Robust Mahalanobis Uzaklığı	median absolute deviation, MAD scale estimator, robust scale estimation, Medyan Mutlak Sapma (MAD) Tahmini	Welch ANOVA, trimmed-mean ANOVA, heteroscedastic one-way ANOVA, Robust ANOVA (Welch & Trimmed Mean)
関連	5	5	5
概要	Robust Mahalanobis Distance flags multivariate outliers by measuring how far each observation lies from the centre of the data using a robust covariance estimate. It builds on the robust-distance framework of Rousseeuw and Van Zomeren (1990) and the multivariate outlier-detection approach of Filzmoser, Garrett and Reimann (2005), replacing the classical mean and covariance with the Minimum Covariance Determinant (MCD) estimate so that the outliers themselves do not distort the distance.	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.	Robust ANOVA compares the central tendency of three or more groups when the classical assumptions of normality and equal variances fail. It combines Welch's heteroscedasticity-adjusted statistic, introduced by Welch in 1951, with trimmed-mean tests advanced by Wilcox, giving reliable comparisons in the presence of outliers and unequal group spreads.