手法を比較

	ロバストANOVA（ウェルチとトリム平均）	最小二乗法 (OLS) 回帰	Theil-Sen推定量
分野	統計学	計量経済学	統計学
系統	Regression model	Regression model	Regression model
提唱年	1951	2019	1968
提唱者	Welch (1951); robust trimmed-mean approach popularised by Wilcox	Wooldridge (textbook treatment); classical least squares	Henri Theil (1950); P. K. Sen (1968)
種類	Robust one-way analysis of variance	Linear regression	Robust linear regression
原典	Welch, B. L. (1951). On the comparison of several mean values: an alternative approach. Biometrika, 38(3/4), 330-336.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860	Sen, P. K. (1968). Estimates of the Regression Coefficient Based on Kendall's Tau. Journal of the American Statistical Association, 63(324), 1379-1389.
別名	Welch ANOVA, trimmed-mean ANOVA, heteroscedastic one-way ANOVA, Robust ANOVA (Welch & Trimmed Mean)	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	Theil-Sen Tahmincisi, Theil-Sen regression, median slope estimator, Sen's slope estimator
関連	5	5	6
概要	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.	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).	The Theil-Sen estimator is a robust linear regression method that estimates the slope as the median of the slopes computed over all pairs of data points. Introduced by Henri Theil in 1950 and extended by P. K. Sen in 1968, it tolerates outliers in the response with a breakdown point of about 29%.