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| 回归与平滑样条× | 多项式回归× | |
|---|---|---|
| 领域≠ | 机器学习 | 统计学 |
| 方法族≠ | Machine learning | Regression model |
| 起源年份≠ | 1996 | 2012 |
| 提出者≠ | Spline regression literature; P-splines by Eilers & Marx | Montgomery, Peck & Vining (textbook treatment); classical least squares |
| 类型≠ | Piecewise-polynomial nonparametric regression | Linear regression in transformed predictors |
| 开创性文献≠ | Eilers, P. H. C., & Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11(2), 89–121. DOI ↗ | Montgomery, D. C., Peck, E. A. & Vining, G. G. (2012). Introduction to Linear Regression Analysis. Wiley. ISBN: 978-0470542811 |
| 别名≠ | splines, cubic splines, natural splines, smoothing splines | polynomial least squares, curvilinear regression, Polinom Regresyonu |
| 相关 | 4 | 4 |
| 摘要≠ | Regression splines model a nonlinear relationship by fitting piecewise polynomials that join smoothly at a set of points called knots. Cubic and natural splines are the most common, and smoothing splines add a roughness penalty that automatically balances fit against smoothness. Splines are the standard flexible building block for univariate nonlinear regression and the basis of generalized additive models. | Polynomial regression is a regression method that models non-linear relationships by including squared and higher-degree terms of an explanatory variable, and it is a core tool of response surface analysis. As developed in Montgomery, Peck and Vining's Introduction to Linear Regression Analysis (2012), it remains linear in its parameters even though the fitted curve bends. |
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