手法を比較

	ロバスト・マハラノビス距離	歪んだ分布に対する調整済み箱ひげ図	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	2008	1951
提唱者	Rousseeuw & Van Zomeren (robust distance); Filzmoser, Garrett & Reimann (multivariate outlier detection)	Hubert & Vandervieren	Welch (1951); robust trimmed-mean approach popularised by Wilcox
種類	Robust multivariate outlier detection	Robust outlier detection / descriptive visualization	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.	Hubert, M. & Vandervieren, E. (2008). An Adjusted Boxplot for Skewed Distributions. Computational Statistics & Data Analysis, 52(12), 5186-5201.	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	adjusted box plot, medcouple boxplot, skewness-adjusted boxplot, Düzeltilmiş Kutu Grafiği (Adjusted Boxplot)	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.	The Adjusted Boxplot is a robust descriptive tool introduced by Hubert and Vandervieren (2008) that corrects the classical IQR-based boxplot for skewness using the medcouple statistic, reducing the false labelling of outliers in asymmetric data.	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.