Theorem 4.7.1 constrains its applicable range to: "If the parameters are identifiable". However, It may also require the constraint of certain regularity conditions. For instance, the maximum statistic (MLE of a Uniform distribution) is identifiable, yet it does not converge to Gaussian distribution.
Theorem 4.7.1 constrains its applicable range to: "If the parameters are identifiable". However, It may also require the constraint of certain regularity conditions. For instance, the maximum statistic (MLE of a Uniform distribution) is identifiable, yet it does not converge to Gaussian distribution.