# Conceptual Question on Least Squares Estimation Method

What is meant by Least square plus Gaussian method of estimating the parameters of an unknown system? I am aware of least squares in general but some works refer it as least square+gaussian method. What is the role of Gaussian here? Is it for some kind of assumption of the distribution of the residual errors? please clarify

• Can you give a link to a paper where this is done? – jan Aug 22 '13 at 18:09
• Maybe what is meant is that in a linear guassian model ML estimation of the parameters leads to the same normal equations as in a least squares estimation formulation... – niaren Aug 22 '13 at 19:58
• See this blogpost: cliquepotential.blogspot.com/2013/05/… – Deniz Dec 21 '13 at 19:01

## 2 Answers

Gauss did a two-way proof. In rough terms, he not only showed that least squares gives the best fit to data containing a standard normal distribution of errors, but that if least squares is always giving the best fit, that implies that the distribution is indeed standard normal (also now called Gaussian).

The correlation coefficient, often computed in conjunction with a least square fit, is usually assumed to be parameterizing an underlying Gaussian distribution. If the distribution is otherwise, it may well infer nonsense.

Least-squares estimator is a maximum likelihood estimator when the errors are have normal (i.e. Gaussian) distribution.

Maybe you mean Gauss-Newton method for solving nonlinear least squares problems.