E1.10 The Weak Law of Large Numbers (Econometrics Math)

In this video, I introduce convergence in probability, prove Chebyshev's inequality and I use the inequality to prove the weak law of large numbers.

This is part of my series of videos that reviews important concepts from mathematical statistics that are useful in econometrics.

For more information on my broader YouTube project or to see a complete listing of my other YouTube videos, check out my video website.

http://sites.google.com/site/intromediateecon/

Category:

Education

Tags:

• convergence in probability
• Chebyshev's inequality
• Chebychev's inequality
• law of large numbers
• weak law of large numbers
• mathematical statistics
• probability
• statistics
• econometrics
• math review for econometrics
• asymptotic theory
• economic

[schwartika]

I believe that the first inequality is Markovs inequality. Though at 6:53 you have reached the Chebychevs inequality. The one with the absolute value and the sigma squared.

[intromediateecon]

@schwartika The way most people distinguish these inequalities, you're right. My TA had the same comment a few months ago on some notes I wrote. It turns out that the text from which I learned these inequalities is Casella and Berger's Statistical Inference. In that book, they have the same naming convention that I have in this video. The rest of the world gives Markov credit whereas Casella and Berger give Markov's Inequality to Chebyshev (as well as Chebyshev's actual inequality).

[feartheterp]

Did you do something wrong in the Chebychev's portion? at 4:24 Should it be P[X>e]<E(x)/e?, not P(X<e)<E(x)/e

[intromediateecon]

@feartheterp Oops! Yes, I did. Thanks for pointing that out. I added some annotations to the video to point this out for future viewers. For the proof, the logic was all in there, but I just flipped the inequality on the inside of the probability statement. Sorry for any confusion that caused.

[eric11998877]

This is a very cool video. Thank you for posting it!!!

I very much appreciate your recent focus on statistics,

and hope that you continue to share your statistical

prowess as it is very helpful in swallowing econometric

concepts. Keep up the good work!!! especially stats :D

[intromediateecon]

@eric11998877 Thanks! I'm glad this is helpful. Short of doing something on regression, do you have any suggestions for topics? When I have time, I'll do something on the Central Limit Theorem, but is there another topic that is genuinely confusing to you (and your friends) in econometrics math?

[wilsq]

@intromediateecon I vote for Mixture Model, EM Algorithm, and Dynamic Linear Models.

[sebaz88]

Hello, thanks for the video, do you talk in any of your videos about Op(1) and op(1)? Thanks!

[LIGHTSAT1]

the way you have edited it is kind of bad. it disturbs. a smooth flowing video would be more welcome.

nevertheless the video is helpful