مقایسهٔ روش‌ها

	کمترین مربعات وزنی غیرخطی (NWLS)	حداقل مربعات تعمیم‌یافته (GLS)	رگرسیون حداقل مربعات وزنی (WLS)
حوزه	اقتصادسنجی	آمار	آمار
خانواده	Regression model	Regression model	Regression model
سال پیدایش	1960s–1980s (formalized in applied econometrics)	1935	1935
پدیدآور	Extension of Gauss-Newton nonlinear least squares with Aitken-type weighting	Alexander Craig Aitken	Alexander Craig Aitken
نوع	Nonlinear regression estimator	Linear estimator	Weighted linear estimator
منبع بنیادین	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.	Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48.
نام‌های دیگر	NWLS, nonlinear weighted least squares, weighted nonlinear regression, heteroscedasticity-corrected nonlinear regression	GLS, Aitken estimator, EGLS, feasible GLS	WLS, weighted regression, heteroscedasticity-corrected OLS, variance-weighted least squares
مرتبط	3	3	3
خلاصه	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.	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.