About: Non-linear least squares

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Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m ≥ n). It is used in some forms of nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations. There are many similarities to linear least squares, but also some significant differences. In economic theory, the non-linear least squares method is applied in (i) the probit regression, (ii) threshold regression, (iii) smooth regression, (iv) logistic link regression, (v) Box-Cox transformed regressors.

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rdfs:label	Mínimos cuadrados no lineales (es) Moindres carrés non linéaires (fr) 非線形最小二乗法 (ja) Non-linear least squares (en)
rdfs:comment	Los Mínimos cuadrados no lineales es la forma de análisis de mínimos cuadrados que se usa para encajar un conjunto de m observaciones con un modelo que es no lineal en n parámetros desconocidos (m > n). Se utiliza en algunas formas de regresión no lineal. La base del método es para aproximar el modelo por uno lineal y para refinar los parámetros por iteraciones sucesivas. Hay muchas similitudes con mínimos cuadrados lineales, pero también algunas diferencias importantes. (es) Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m ≥ n). It is used in some forms of nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations. There are many similarities to linear least squares, but also some significant differences. In economic theory, the non-linear least squares method is applied in (i) the probit regression, (ii) threshold regression, (iii) smooth regression, (iv) logistic link regression, (v) Box-Cox transformed regressors. (en) Les moindres carrés non linéaires est une forme des moindres carrés adaptée pour l'estimation d'un modèle non linéaire en n paramètres à partir de m observations (m > n). Une façon d'estimer ce genre de problème est de considérer des itérations successives se basant sur une version linéarisée du modèle initial. (fr) 非線形最小二乗法（ひせんけいさいしょうにじょうほう、英: non-linear least squares）とは、観測データに対するカーブフィッティング手法の一つであり、最小二乗法を非線形なモデル関数に拡張したものである。非線形最小二乗法は、未知パラメータ（フィッティングパラメータ）を非線形の形で持つ関数モデルを用いて、観測データを記述すること、すなわち、データに最も当てはまりの良いフィッティングパラメータを推定することを目的とする。 (ja)
dct:subject	Least squares
Wikipage page ID	15652764 (xsd:integer)
Wikipage revision ID	1103186857 (xsd:integer)
Link from a Wikipage to another Wikipage	Quadratic function Numerical Recipes Variance Davidon–Fletcher–Powell formula Levenberg–Marquardt algorithm Conjugate gradient method Maxima and minima Gauss–Newton algorithm Nelder–Mead method Orthogonal Optimization (mathematics) Ellipse Gradient Log-normal distribution Cholesky decomposition Simplex Singular value decomposition Computer simulation Linear least squares (mathematics) Semi-log plot Cauchy distribution Trace (linear algebra) Errors and residuals in statistics Least squares Line search Lineweaver–Burk plot Curve fitting Parabola Diagonal matrix Nonlinear regression QR decomposition Jacobian matrix and determinant Taylor series Block matrix Least squares Hessian matrix Positive-definite matrix Grey box model Newton's method in optimization Orthogonal matrix Michaelis–Menten kinetics Nonlinear programming Polytope Least squares support vector machine Steepest descent Round-off
Link from a Wikipage to an external page	https://archive.siam.org/books/textbooks/fr18_book.pdf
sameAs	Non-linear least squares Non-linear least squares Non-linear least squares Non-linear least squares Non-linear least squares Non-linear least squares Non-linear least squares
dbp:wikiPageUsesTemplate	dbt:Regression_bar dbt:Cite_book dbt:Main dbt:Math dbt:Mvar dbt:Reflist dbt:Least_Squares_and_Regression_Analysis
has abstract	Los Mínimos cuadrados no lineales es la forma de análisis de mínimos cuadrados que se usa para encajar un conjunto de m observaciones con un modelo que es no lineal en n parámetros desconocidos (m > n). Se utiliza en algunas formas de regresión no lineal. La base del método es para aproximar el modelo por uno lineal y para refinar los parámetros por iteraciones sucesivas. Hay muchas similitudes con mínimos cuadrados lineales, pero también algunas diferencias importantes. (es) Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m ≥ n). It is used in some forms of nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations. There are many similarities to linear least squares, but also some significant differences. In economic theory, the non-linear least squares method is applied in (i) the probit regression, (ii) threshold regression, (iii) smooth regression, (iv) logistic link regression, (v) Box-Cox transformed regressors. (en) Les moindres carrés non linéaires est une forme des moindres carrés adaptée pour l'estimation d'un modèle non linéaire en n paramètres à partir de m observations (m > n). Une façon d'estimer ce genre de problème est de considérer des itérations successives se basant sur une version linéarisée du modèle initial. (fr) 非線形最小二乗法（ひせんけいさいしょうにじょうほう、英: non-linear least squares）とは、観測データに対するカーブフィッティング手法の一つであり、最小二乗法を非線形なモデル関数に拡張したものである。非線形最小二乗法は、未知パラメータ（フィッティングパラメータ）を非線形の形で持つ関数モデルを用いて、観測データを記述すること、すなわち、データに最も当てはまりの良いフィッティングパラメータを推定することを目的とする。 (ja)
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is Link from a Wikipage to another Wikipage of	Pseudo-range multilateration List of aqueous ions by element NLS M-estimator Non-linear least-squares estimation Nonlinear Least Squares Hyperpolarized carbon-13 MRI Ridge regression Levenberg–Marquardt algorithm

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