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| Robuste Regression× | Least Trimmed Squares (LTS)-Regression× | |
|---|---|---|
| Fachgebiet | Statistik | Statistik |
| Familie | Regression model | Regression model |
| Entstehungsjahr≠ | 1964 | 1984 |
| Urheber≠ | Peter J. Huber (M-estimation, 1964); Frank Hampel (influence function, 1974) | Peter J. Rousseeuw |
| Typ≠ | Regression with outlier resistance | Robust linear regression |
| Wegweisende Quelle≠ | Huber, P. J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), 73–101. DOI ↗ | Rousseeuw, P. J. (1984). Least Median of Squares Regression. Journal of the American Statistical Association, 79(388), 871-880. DOI ↗ |
| Aliasnamen≠ | M-estimation regression, robust linear regression, outlier-resistant regression, MM-estimation | LTS, least trimmed squares regression, trimmed least squares, robust regression |
| Verwandt≠ | 6 | 5 |
| Zusammenfassung≠ | Robust regression estimates the linear relationship between a continuous outcome and predictors while sharply reducing the influence of outliers and leverage points. Unlike OLS, which is highly sensitive to extreme observations, robust methods assign down-weighted influence to atypical data points, producing coefficient estimates that remain stable even when a fraction of the data is contaminated or non-normally distributed. | 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. |
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