In page 3, of Asymptotic Theory for Econometricians, the following assumptions of OLS are defined:
- OLS model: $Y= X\beta+\epsilon$
- $X$ is a nonstochastic and finite n x k matrix, n > k.
- $X'X$ is nonsingular.
- $\epsilon \sim N(0, \sigma^2I)$, $\sigma^2 < \infty$
Given 1-5, $Efficiency$ of $ \hat \beta $ is the maximum likelihood estimator and is the best unbiased estimator in the sense that the variance covariance matrix of any other unbiased estimator exceeds that of $ \hat \beta $ by a positive semidefinite matrix, regardless of the value of $ \hat \beta $.
Could anynone provide an intuitive explanation for this definition?