方法对比
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| W-估计量稳健回归（Welsch / Tukey Bisquare）× | MM估计量稳健回归× | 普通最小二乘法 (OLS) 回归× | |
|---|---|---|---|
| 领域≠ | 统计学 | 统计学 | 计量经济学 |
| 方法族 | Regression model | Regression model | Regression model |
| 起源年份≠ | 1974 | 1987 | 2019 |
| 提出者≠ | Beaton & Tukey (bisquare weight); Welsch (Welsch weight) | Victor J. Yohai | Wooldridge (textbook treatment); classical least squares |
| 类型≠ | Robust regression (redescending M-estimator) | Robust linear regression | Linear regression |
| 开创性文献≠ | 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 ↗ | Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860 |
| 别名 | 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 | ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu |
| 相关≠ | 4 | 5 | 5 |
| 摘要≠ | 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. | 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). |
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