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| Robust Ridge Regression× | Robust Regression× | |
|---|---|---|
| Fagområde | Statistik | Statistik |
| Familie | Regression model | Regression model |
| Oprindelsesår≠ | 1991 | 1964 |
| Ophavsperson≠ | Silvapulle (1991); building on Tikhonov (1963) and Huber (1964) | Peter J. Huber (M-estimation, 1964); Frank Hampel (influence function, 1974) |
| Type≠ | Regularized robust linear regression | Regression with outlier resistance |
| Oprindelig kilde≠ | Silvapulle, M. J. (1991). Robust ridge regression based on an M-estimator. Australian Journal of Statistics, 33(3), 319–333. link ↗ | Huber, P. J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), 73–101. DOI ↗ |
| Aliasser | ridge M-estimation, robust regularized regression, M-estimator ridge, outlier-resistant ridge regression | M-estimation regression, robust linear regression, outlier-resistant regression, MM-estimation |
| Relaterede≠ | 5 | 6 |
| Resumé≠ | Robust Ridge regression combines M-estimation with L2 (ridge) regularization to produce coefficient estimates that are simultaneously resistant to outliers and stable under multicollinearity. It minimizes a robust loss function (such as Huber's) penalized by the squared norm of the coefficient vector, downweighting influential observations while shrinking correlated predictors toward zero. | 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. |
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