Non-linear least squares

Non-linear least squares is the form of <a href="/facts/Least_squares/50jIwbxC">least squares</a> 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 <a href="/facts/Nonlinear_regression/8mMuJSe8">nonlinear regression</a>. 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 <a href="/facts/Linear_least_squares_(mathematics)/dKctFUCV">linear least squares</a>, but also some <a href="/facts/Least_squares/50jIwbxC">significant differences</a>. 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 (
 
 
 
 m
 (
 x
 ,
 
 θ
 
 i
 
 
 )
 =
 
 θ
 
 1
 
 
 +
 
 θ
 
 2
 
 
 
 x
 
 (
 
 θ
 
 3
 
 
 )
 
 
 
 
 {\displaystyle m(x,\theta _{i})=\theta _{1}+\theta _{2}x^{(\theta _{3})}}
 
).

Non-linear least squares open-in-new

Non-linear least squares