E1.11: Applying the Continuous Mapping Theorem (Econometrics Math)

This video demonstrates how to apply the continuous mapping theorem to make a consistency argument for a rather wide class of estimators. In particular, I show that any continuous function of a sample mean can be given a consistency argument through the continuous mapping theorem.
This is a powerful theorem that can show under quite weak assumptions that our estimators have the desirable property of consistency.
This is part of my series of math review for econometrics videos. These are the videos labeled with an E at the start of the title on my channel.

[@lifesbetteronaboard]

Still a fantastic resource 10 years later. Thank you!

[@jamiecross100]

This is an excellent video! Very helpful!

[@bobo0612]

thank you for the excellent explanation

[@intromediateecon]

That is LyX, a free LaTeX typesetting program. I actually prefer it over Word or Word Perfect when I need to type up nice-looking academic documents. I apologize for the delay in responding to comments. Life happens.

[@Matteo-uq7gc]

Fantastic video thanks!

[@certainperfectratio]

Very helpful. Thank you

[@jakobforslin6301]

Thanks a lot!

[@crystalzang9316]

what about finding the asymptotic distribution of log(X) where X follows an asymptotic normal distribution (x>0)? How to handle the variance?

[@intromediateecon]

@mrvrabie Me too :) Thanks for the feedback.