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| Hồi quy tuyến tính bội vững chắc× | Hồi quy tuyến tính bội× | |
|---|---|---|
| Lĩnh vực | Thống kê | Thống kê |
| Họ | Regression model | Regression model |
| Năm ra đời≠ | 1964–1980s | 1886 |
| Người khởi xướng≠ | Peter J. Huber (M-estimators, 1964); extended by Rousseeuw, Yohai, and Maronna | Francis Galton; formalized by Karl Pearson |
| Loại≠ | Robust linear regression | Parametric linear model |
| Công trình gốc≠ | Huber, P. J. (1964). Robust estimation of a location parameter. Annals of Mathematical Statistics, 35(1), 73–101. DOI ↗ | Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263. DOI ↗ |
| Tên gọi khác≠ | robust MLR, M-estimator regression, resistant multiple regression, robust OLS | MLR, OLS regression, multiple regression, linear regression with multiple predictors |
| Liên quan≠ | 6 | 8 |
| Tóm tắt≠ | Robust multiple linear regression estimates the linear relationship between a continuous outcome and several predictors while being resistant to outliers and violations of the normality assumption. Instead of minimising the sum of squared residuals, it uses a bounded loss function — most commonly Huber's or Tukey's bisquare — so that extreme observations receive limited influence on the estimated coefficients. | Multiple linear regression (MLR) is a parametric regression model that expresses a continuous outcome as a weighted linear combination of two or more predictor variables plus a random error term. The unknown weights (regression coefficients) are estimated by ordinary least squares (OLS), which minimises the sum of squared residuals. The method traces to Francis Galton's 1886 work on hereditary stature and was placed on firm mathematical footing by Karl Pearson; Draper and Smith's 1966 textbook established it as the standard framework for applied regression. |
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