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| Estymatory M (regresja odporna)× | Regresja metodą najmniejszych przyciętych kwadratów (LTS)× | Regresja metodą najmniejszych kwadratów (OLS)× | |
|---|---|---|---|
| Dziedzina≠ | Statystyka | Statystyka | Ekonometria |
| Rodzina | Regression model | Regression model | Regression model |
| Rok powstania≠ | 2009 | 1984 | 2019 |
| Twórca≠ | Peter J. Huber | Peter J. Rousseeuw | Wooldridge (textbook treatment); classical least squares |
| Typ≠ | Robust linear regression | Robust linear regression | Linear regression |
| Źródło pierwotne≠ | Huber, P. J., & Ronchetti, E. M. (2009). Robust Statistics (2nd ed.). Wiley. link ↗ | Rousseeuw, P. J. (1984). Least Median of Squares Regression. Journal of the American Statistical Association, 79(388), 871-880. DOI ↗ | Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860 |
| Inne nazwy≠ | m-estimation, huber regression, robust m-regression, M-Tahmin Ediciler | LTS, least trimmed squares regression, trimmed least squares, robust regression | ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu |
| Pokrewne | 5 | 5 | 5 |
| Podsumowanie≠ | M-estimators are a robust generalisation of maximum likelihood estimation, formalised in the work of Peter J. Huber (Huber & Ronchetti, 2009). Instead of squaring every residual, they apply a bounded loss function so that large residuals from outliers are down-weighted rather than allowed to dominate the fit. | Least Trimmed Squares is a robust linear regression method introduced by Peter J. Rousseeuw in 1984. Instead of fitting all residuals, it estimates the coefficients by minimising the sum of only the h smallest squared residuals, which gives it a breakdown point of up to 50% and reliable estimates on data heavily contaminated by outliers. | 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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