Statement: if $\hat{\theta}$ is the MLE of some parameter $\theta$ then asymptotically $\hat{\theta} \sim \mathcal{N}(\theta, I_\theta^{-1}),$ where $I_\theta$ is the fisher information matrix.
My question is, what if $\hat{\theta}$ is a biased estimator of $\theta$? Surely $\mu$ will not be $\theta$ then.
