مقایسهٔ روشها
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| تخمینگر W: رگرسیون مقاوم (وزنهای ولش / توکی بایاسکوئر)× | رگرسیون حداقل مربعات معمولی (OLS)× | تخمینگر تیل-سن× | |
|---|---|---|---|
| حوزه≠ | آمار | اقتصادسنجی | آمار |
| خانواده | Regression model | Regression model | Regression model |
| سال پیدایش≠ | 1974 | 2019 | 1968 |
| پدیدآور≠ | Beaton & Tukey (bisquare weight); Welsch (Welsch weight) | Wooldridge (textbook treatment); classical least squares | Henri Theil (1950); P. K. Sen (1968) |
| نوع≠ | Robust regression (redescending M-estimator) | Linear regression | Robust linear regression |
| منبع بنیادین≠ | 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 ↗ | 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. DOI ↗ |
| نامهای دیگر≠ | Tukey bisquare M-estimator, Welsch M-estimator, redescending M-estimator, W-Tahmin Edici (Welsch / Tukey Bisquare) | 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 |
| مرتبط≠ | 4 | 5 | 6 |
| خلاصه≠ | 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. | 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%. |
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