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I have noticed that a lot of statistics textbooks contain lengthy discussions and detailed proofs on showing that MLE estimates are asymptotically normal (under regularity conditions).

On the other hand they seem to deal with Method of Moments estimates much more casually by usually just stating it as a an obvious fact that MoM estimates are asymptotically normal.

How can I actually prove this? Is it just a simple consequence of the Delta method? Are there any resources that present the proof?

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  • $\begingroup$ I suspect the Central Limit Theorem may have an immediate bearing on this question, depending on just how general you take the "method of moments" to be. $\endgroup$ – whuber Feb 19 '19 at 14:10

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