Is the difference between an OLS regression and a GLS regression qualitative or quantitative?

1 Answer
Yonas Yohannes
Feb 14, 2016

It is quantitative

Explanation:

Ordinary least squares is a technique for estimating unknown parameters in a linear regression model. OLS yield the maximum likelihood in a vector #β#, assuming the parameters have equal variance and are uncorrelated, in a noise ε - homoscedastic.

#vec(y)=Xvec(β)+vec(ε)#

Generalized least squares allows this approach to be generalized to give the maximum likelihood estimate #β# when the noise is of unequal variance (heteroscedasticity). Typically this leads to mathematical treatment that presents the two as follows:
OLS: #vecY=Xbeta+ε " where " ε~N(0,σ²I)#
GLS: #vecY=Xbeta+η " where " η~N(0,σ²Cov)#
Note the formulation for the two approaches results in real structural and quantitative difference. Notice the two are governed by two different Gauss distribution the
#N(0, sigma^2M); M = I " or " M=Cov# part
Where: #I = # "Identity Matrix and " #Cov =# "Covariance Matrix

Cheers!

Related questions
See all questions in Least Squares Regression Line (LSRL)
Impact of this question
28724 views around the world
You can reuse this answer
Creative Commons License