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| MM-estimering for robust regression× | Almindelig mindste kvadraters metode (OLS) regression× | Theil-Sen Estimator× | |
|---|---|---|---|
| Fagområde≠ | Statistik | Økonometri | Statistik |
| Familie | Regression model | Regression model | Regression model |
| Oprindelsesår≠ | 1987 | 2019 | 1968 |
| Ophavsperson≠ | Victor J. Yohai | Wooldridge (textbook treatment); classical least squares | Henri Theil (1950); P. K. Sen (1968) |
| Type≠ | Robust linear regression | Linear regression | Robust linear regression |
| Oprindelig kilde≠ | 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 | 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 ↗ |
| Aliasser≠ | 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 | Theil-Sen Tahmincisi, Theil-Sen regression, median slope estimator, Sen's slope estimator |
| Relaterede≠ | 5 | 5 | 6 |
| Resumé≠ | 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). | 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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