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| Regresja odporna z estymatorem W (Welsch / Tukey Bisquare)× | Estymacja MM dla regresji odpornej× | Estymator Theila-Sena× | |
|---|---|---|---|
| Dziedzina | Statystyka | Statystyka | Statystyka |
| Rodzina | Regression model | Regression model | Regression model |
| Rok powstania≠ | 1974 | 1987 | 1968 |
| Twórca≠ | Beaton & Tukey (bisquare weight); Welsch (Welsch weight) | Victor J. Yohai | Henri Theil (1950); P. K. Sen (1968) |
| Typ≠ | Robust regression (redescending M-estimator) | Robust linear regression | Robust linear regression |
| Źródło pierwotne≠ | Beaton, A. E. & Tukey, J. W. (1974). The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data. Technometrics, 16(2), 147-185. DOI ↗ | Yohai, V. J. (1987). High Breakdown-Point and High Efficiency Robust Estimates for Regression. Annals of Statistics, 15(2), 642-656. DOI ↗ | Sen, P. K. (1968). Estimates of the Regression Coefficient Based on Kendall's Tau. Journal of the American Statistical Association, 63(324), 1379-1389. DOI ↗ |
| Inne nazwy≠ | Tukey bisquare M-estimator, Welsch M-estimator, redescending M-estimator, W-Tahmin Edici (Welsch / Tukey Bisquare) | MM-estimation, MM robust regression, high-breakdown high-efficiency estimator, MM-Tahmin Edici | Theil-Sen Tahmincisi, Theil-Sen regression, median slope estimator, Sen's slope estimator |
| Pokrewne≠ | 4 | 5 | 6 |
| Podsumowanie≠ | The W-estimator is a family of robust M-estimator variants for linear regression that use the Tukey bisquare and Welsch weight functions, introduced in the line of work going back to Beaton and Tukey (1974). Because its weights fall rapidly toward zero as a residual grows, it resists outliers more strongly than the Huber M-estimator. | The MM-estimator is a robust linear regression method introduced by Victor J. Yohai in 1987. It combines the high breakdown point of an S-estimator with the high efficiency of an M-estimator, so it resists outliers strongly while still using the data efficiently when errors are well-behaved. | 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%. |
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