方法对比
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| 非线性OLS（非线性最小二乘法）× | 最大似然估计× | |
|---|---|---|
| 领域≠ | 计量经济学 | 统计学 |
| 方法族 | Regression model | Regression model |
| 起源年份≠ | 1974–1987 | 1922 |
| 提出者≠ | Gallant (1987); Wooldridge (2010) for econometric treatment | R. A. Fisher |
| 类型≠ | Nonlinear regression estimator | Parametric point estimator |
| 开创性文献≠ | Gallant, A. R. (1987). Nonlinear Statistical Models. John Wiley & Sons. ISBN: 978-0471802600 | Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London, Series A, 222, 309–368. DOI ↗ |
| 别名 | nonlinear least squares, NLS, NLLS, nonlinear regression | MLE, maximum-likelihood estimator, ML estimation, Fisher's method of maximum likelihood |
| 相关≠ | 5 | 4 |
| 摘要≠ | 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. | Maximum Likelihood Estimation (MLE) is a general-purpose parametric method for estimating the unknown parameters of a statistical model by finding the parameter values that make the observed data most probable. Formalized by R. A. Fisher in his landmark 1922 paper in the Philosophical Transactions of the Royal Society, MLE has become the dominant parameter-estimation paradigm in modern statistics and is the foundational engine behind logistic regression, generalized linear models, structural equation modeling, and virtually all parametric inference procedures. |
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