Mathematical Statistics (2024): Lecture 25

Proving properties of MLEs

In this video:
🔹 Jensen's Inequality 0:18
🔹 Recap of the Nice Properties of MLEs 8:30
🔹 Proof that MLEs are Consistent Estimators 16:40
🔹 Proof that MLEs are Asymptotically Unbiased 33:43
🔹 An Interesting MLE Example 50:35

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[AbhijitGuptamjj]

Thanks for another fantastic lecture, Professor! I was wondering if, having proved the asymptotic properties of MLE, particularly the asymptotic distribution, we could use that to devise an alternative proof for asymptotic unbiasedness?

[thatsfantastic]

Another beautiful lecture!. And, that problem carries a massive amount of elegance in it. Surprisingly, I was able to solve that problem on my own :-D but I don't know why I solved it like, P(y = 0) = int(0 to c) f(x) dx, the other way. Maybe, because I thought that I need, this much percentage of area(i.e. 0's) below c in expo(rate=lambda). But that was quite a fun! as always.

[ritardstrength]

Is this a one- or two-semester course?