I am currently studying the properties of the Maximum Likelihood Estimator. One of these properties being the asymptotic normality, I found the following equation:
$$\sqrt{n}(\hat{\theta} - \theta_{0}) \rightarrow N(0, {I(\theta_{0})}^{-1}) \text{ as } n \rightarrow \infty$$
where $\hat{\theta}$ is the maximum likelihood estimator of $\theta$, $I(\theta_{0})^{-1}$ is the Fisher information and $\theta_{0}$ is the 'true value of the parameter $\theta$'. However, it is not explained exactly what that means. Also, why should this 'true value' be in the formula? Would it not suffice to just use $\theta$ instead of $\theta_{0}$? I hope someone can clarify this for me.