手法を比較

	ロバストANOVA（ウェルチとトリム平均）	ブートストラップ推論	Theil-Sen推定量
分野	統計学	統計学	統計学
系統	Regression model	Regression model	Regression model
提唱年	1951	1979	1968
提唱者	Welch (1951); robust trimmed-mean approach popularised by Wilcox	Bradley Efron	Henri Theil (1950); P. K. Sen (1968)
種類	Robust one-way analysis of variance	Resampling-based inference	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.	Efron, B. (1979). Bootstrap Methods: Another Look at the Jackknife. Annals of Statistics, 7(1), 1-26.	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)	bootstrap, bootstrap resampling, nonparametric bootstrap, Bootstrap Çıkarımı	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.	Bootstrap inference, introduced by Bradley Efron in 1979, estimates the sampling distribution of a statistic by repeatedly resampling the observed data with replacement. It requires no distributional assumption and produces reliable confidence intervals even in small samples.	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%.