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Weighted least squares (WLS), also known as weighted linear regression, [1] [2] is a generalization of ordinary least squares and linear regression in which knowledge of the unequal variance of observations (heteroscedasticity) is incorporated into the regression.
The method of iteratively reweighted least squares (IRLS) is used to solve certain optimization problems with objective functions of the form of a p-norm: = | |, by an iterative method in which each step involves solving a weighted least squares problem of the form: [1]
Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression , including variants for ordinary (unweighted), weighted , and generalized (correlated) residuals .
The result of fitting a set of data points with a quadratic function Conic fitting a set of points using least-squares approximation. In regression analysis, least squares is a parameter estimation method based on minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each ...
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.
Moving least squares is a method of reconstructing continuous functions from a set of unorganized point samples via the calculation of a weighted least squares measure biased towards the region around the point at which the reconstructed value is requested.
The original problem is therefore equivalent to the nonlinear least squares problem of minimizing () with respect to . For this purpose standard optimization methods, e.g. the Levenberg-Marquardt algorithm can be used. Matlab implementation of the variable projections algorithm for weighted low-rank approximation:
SmartPLS is a software with graphical user interface for variance-based structural equation modeling (SEM) using the partial least squares (PLS) path modeling method ...