Mathematical Statistics (2024): Lecture 14

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The Delta Method for pushing functions through asymptotic normaility!

In this video:
🔹 Some IID non-Specified Distribution Notation 1:10
🔹 The Delta Method for Pushing Asymptotic Normality Through Functions 2:45
🔹 A Delta Method Example 9:55
🔹 Proof of the Delta Method 20:55
🔹 The Asymptotic Distribution of the Sample Variance 40:02

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Hi. A sample mean is asymptotically normal, which means it converges in distribution to N(0, 1) (taken from the definition, and after some scaling). But we have also learnt that the sample mean converges both in probability and in distribution to a constant. And a constant is not N(0, 1). I don't know how to reconcile these two facts and where do I make the error?

lukasuhl
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More details on asymptotic normaility please!

jayfarrell