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| 非線形加重最小二乗法 (NWLS)× | 一般化最小二乗法 (GLS)× | |
|---|---|---|
| 分野≠ | 計量経済学 | 統計学 |
| 系統 | Regression model | Regression model |
| 提唱年≠ | 1960s–1980s (formalized in applied econometrics) | 1935 |
| 提唱者≠ | Extension of Gauss-Newton nonlinear least squares with Aitken-type weighting | Alexander Craig Aitken |
| 種類≠ | Nonlinear regression estimator | Linear estimator |
| 原典≠ | 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 ↗ |
| 別名≠ | NWLS, nonlinear weighted least squares, weighted nonlinear regression, heteroscedasticity-corrected nonlinear regression | GLS, Aitken estimator, EGLS, feasible GLS |
| 関連 | 3 | 3 |
| 概要≠ | 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. | Generalized Least Squares (GLS) is a linear regression estimator that extends ordinary least squares to handle situations where the error terms are correlated or have non-constant variance (heteroscedasticity). Introduced by Alexander Craig Aitken in 1935, GLS achieves the Best Linear Unbiased Estimator (BLUE) under a general error covariance structure by weighting observations according to their precision, providing a theoretical bridge between OLS and modern linear mixed models. |
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