Gauss Markov Theorem
Overview
The Gauss Markov Theorem is often used to justify the use of OLS Regression.
Best Linear Unbiased Estimator
An estimator is a linear estimator if it is a linear function of a random variable.
{% \hat{y} = a + by %}
It is unbiased if
{% \mathbb{E}[\hat{y}] = y %}
and it is the best estimator of a class, if it has the smallest variance of the estimators of that class.
Gauss Markov Theorem
The Gauss Markov Theorem states that given the assumptions of the classical regression model, the regression
coefficients are the best linear unbiased estimators of the true coefficients. (BLUE)
