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| Diagnostik der Einflussnahme (Cook'sche Distanz, DFFITS, Hebelwirkung)× | Robuste Regression× | |
|---|---|---|
| Fachgebiet | Statistik | Statistik |
| Familie | Regression model | Regression model |
| Entstehungsjahr≠ | 1977 | 1964 |
| Urheber≠ | R. Dennis Cook (Cook's distance); Belsley, Kuh & Welsch (DFFITS, leverage) | Peter J. Huber (M-estimation, 1964); Frank Hampel (influence function, 1974) |
| Typ≠ | Regression diagnostic | Regression with outlier resistance |
| Wegweisende Quelle≠ | Cook, R. D. (1977). Detection of Influential Observations in Linear Regression. Technometrics, 19(1), 15-18. DOI ↗ | Huber, P. J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), 73–101. DOI ↗ |
| Aliasnamen≠ | Cook's distance, DFFITS, leverage, influential observation detection | M-estimation regression, robust linear regression, outlier-resistant regression, MM-estimation |
| Verwandt≠ | 5 | 6 |
| Zusammenfassung≠ | Influence diagnostics are a family of post-fit measures that quantify how much each single observation affects a fitted regression. Cook's distance was introduced by R. Dennis Cook in 1977, with leverage and DFFITS formalised by Belsley, Kuh and Welsch in 1980, to flag the observations that most strongly pull the estimated coefficients. | 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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