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| 非線形最小二乗法（非線形OLS）× | 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≠ | 1974–1987 | 1935 |
| 提唱者≠ | Gallant (1987); Wooldridge (2010) for econometric treatment | Alexander Craig Aitken |
| 種類≠ | Nonlinear regression estimator | Linear estimator |
| 原典≠ | Gallant, A. R. (1987). Nonlinear Statistical Models. John Wiley & Sons. ISBN: 978-0471802600 | 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≠ | nonlinear least squares, NLS, NLLS, nonlinear regression | GLS, Aitken estimator, EGLS, feasible GLS |
| 関連≠ | 5 | 3 |
| 概要≠ | Nonlinear Ordinary Least Squares (NLS) estimates regression models in which the conditional mean function is nonlinear in the parameters. Like standard OLS it minimises the sum of squared residuals, but because no closed-form solution exists the estimator is found by iterative numerical optimisation. Under standard regularity conditions NLS is consistent and asymptotically normal. | 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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