方法对比
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| 非线性加权最小二乘法 (NWLS)× | 加权最小二乘法 (WLS)× | |
|---|---|---|
| 领域≠ | 计量经济学 | 统计学 |
| 方法族 | Regression model | Regression model |
| 起源年份≠ | 1960s–1980s (formalized in applied econometrics) | 1935 |
| 提出者≠ | Extension of Gauss-Newton nonlinear least squares with Aitken-type weighting | Alexander Craig Aitken |
| 类型≠ | Nonlinear regression estimator | Weighted linear estimator |
| 开创性文献≠ | Greene, W. H. (2018). Econometric Analysis (8th ed.). Pearson Education. ISBN: 978-0134461366 | Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48. DOI ↗ |
| 别名 | NWLS, nonlinear weighted least squares, weighted nonlinear regression, heteroscedasticity-corrected nonlinear regression | WLS, weighted regression, heteroscedasticity-corrected OLS, variance-weighted least squares |
| 相关 | 3 | 3 |
| 摘要≠ | Nonlinear Weighted Least Squares combines the flexibility of nonlinear regression with the variance-stabilizing power of observation-level weights. It minimises a weighted sum of squared residuals around a user-specified nonlinear mean function, making it the method of choice when the relationship is inherently nonlinear and error variance differs across observations. | Weighted Least Squares is a generalization of Ordinary Least Squares (OLS) regression that assigns each observation a weight inversely proportional to its error variance, thereby down-weighting high-variance data points and up-weighting precise ones. Introduced in its general matrix form by Alexander Craig Aitken in 1935, WLS is the canonical remedy when heteroscedasticity is present and the error variance structure is known or can be reliably estimated. |
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