Past exam of the options I course of the University of Oxford / 2011 / O / 1 / a / ii

Under the standard consistency and regularity hypotheses for the maximum-likelihood estimator,Equivalently, for large samples $\hat{\theta }$ is approximately $N(\theta ,I_n(\theta {)}^{-1})$. In a standard-error estimate, the unknown parameter in the information may be replaced by the consistent estimate $\hat{\theta }$.