Does asymptotic normality imply consistency?
Update: Asymptotic normality implies consistency, as proven in this quesiton: Showing that asymptotic normality implies consistency.
2026-03-28 05:20:38.1774675238
Asymptotic normality implies consistency?
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Take any example of a consistent and asymptotically normal estimator $\hat\theta_n$ and spoil it like this: $\tilde\theta_n=\hat\theta_n+\frac{1}{n^{1/3}}$.