مقایسهٔ روش‌ها

	فاصله ماهالانوبیس مقاوم	رگرسیون حداقل مربعات هرس‌شده (LTS)	ANOVAی ناپارامتریک (میانگین ناپارامتریک ولش و میانگین هرس‌شده)
حوزه	آمار	آمار	آمار
خانواده	Regression model	Regression model	Regression model
سال پیدایش	1990	1984	1951
پدیدآور	Rousseeuw & Van Zomeren (robust distance); Filzmoser, Garrett & Reimann (multivariate outlier detection)	Peter J. Rousseeuw	Welch (1951); robust trimmed-mean approach popularised by Wilcox
نوع	Robust multivariate outlier detection	Robust linear regression	Robust one-way analysis of variance
منبع بنیادین	Rousseeuw, P. J. & Van Zomeren, B. C. (1990). Unmasking Multivariate Outliers and Leverage Points. Journal of the American Statistical Association, 85(411), 633-639.	Rousseeuw, P. J. (1984). Least Median of Squares Regression. Journal of the American Statistical Association, 79(388), 871-880.	Welch, B. L. (1951). On the comparison of several mean values: an alternative approach. Biometrika, 38(3/4), 330-336.
نام‌های دیگر	MCD Mahalanobis distance, robust mahalanobis, minimum covariance determinant distance, Robust Mahalanobis Uzaklığı	LTS, least trimmed squares regression, trimmed least squares, robust regression	Welch ANOVA, trimmed-mean ANOVA, heteroscedastic one-way ANOVA, Robust ANOVA (Welch & Trimmed Mean)
مرتبط	5	5	5
خلاصه	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.	Least Trimmed Squares is a robust linear regression method introduced by Peter J. Rousseeuw in 1984. Instead of fitting all residuals, it estimates the coefficients by minimising the sum of only the h smallest squared residuals, which gives it a breakdown point of up to 50% and reliable estimates on data heavily contaminated by outliers.	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.