Says the Ordinary Least Squares estimator is the
- Best – Minimum variance in the class of …
- Linear – Can be written as a linear (affine) function of y
- Unbiased – Zero bias. Where bias is $E(\widehat\theta) – \theta $. The regression coefficient’s expected value minus its true value. $E(\widehat\theta) – \theta = 0$.
- Estimator of the regression coefficient $\beta$
While other linear unbiased estimators $\tilde \beta$ do exist, none of them is more efficient than $\widehat\beta$ the Ordinary Least Squares estimator. For these other $\tilde \beta$ estimators,