Fitting Data with Different Error Models
Béla Paláncz · The Mathematica Journal · 2014
A maximum likelihood estimator has been applied to find regression parameters of a straight line in case of different error models.Assuming Gaussian-type noise for the measurement errors, explicit results for the parameters can be given employing Mathematica.In the case of the ordinary least squares (OLS y ), total least squares (TLS), and least geometric mean deviation (LGMD) approaches, as well as the error model of combining ordinary least squares (OLS x and OLS y ) in the Pareto sense, simple formulas are given to compute the parameters via a reduced Gröbner basis.Numerical examples illustrate the methods, and the results are checked via direct global minimization of the residuals.