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What is the condition for $Var(\sqrt{n}(\hat\theta-\theta))\to V$ as $n\to \infty$, where $V$ is the asymptotic variance of $\sqrt{n}(\hat\theta-\theta)$. That is $\sqrt{n}(\hat\theta-\theta))\to^D N(0,V)$.

I ask this since in general convergence in distribution does not imply convergence in moments.

Joe Li
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  • Have you searched "asymptotic variance"? Look at "Asymptotic normality" in [here](http://en.wikipedia.org/wiki/Estimator). – Stat Mar 07 '15 at 02:07
  • Thanks @Stat. But my question is about when the limit of finite sample moment converges to the asymptotic one. I cannot find answer in the link above. – Joe Li Mar 07 '15 at 02:31

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