The Gauss-Markov Theorem proof - matrix form - part 1
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- Опубліковано 6 вер 2024
- This video is the first in a series of videos where we prove the Gauss-Markov Theorem, using the matrix formulation of econometrics. Check out ben-lambert.co... for course materials, and information regarding updates on each of the courses. Quite excitingly (for me at least), I am about to publish a whole series of new videos on Bayesian statistics on youtube. See here for information: ben-lambert.co... Accompanying this series, there will be a book: www.amazon.co....
Hi, sorry for the late reply - have been quite busy. The reason we add Dy rather than just D is that we need to use the sample data in order to construct our estimator. If we just added D arbitrarily then it wouldn't be using the sample data. Hope that helps! Thanks, Ben
could you kindly explain why we need to add Dy? and what's the difference between Beta hat and Beta Tilde? Thanks~
This video explained one critical thing left in my mind after reading through Greene (2003) and Hayashi (2000) 's proof of G-M theorem.
Why do we add Dy to Beta Tilde? This step seems kind of arbitrary to me. Why do that instead of performing some other operation on the original least squares estimator (maybe multiply it by a constant or subtract Dy or something)?
It's just a consequence of the "Linear" assumption in BLUE, i.e. if the model is linear in parameters, it means that the estimator is a linear combination of y's. So any other estimator would have to also be a linear combination of y's, say VY - and you could separate it to the OLS estimator + something else, i.e. (Beta + D)Y = Beta*Y + DY.
Shouldn't you, if you work with the zero conditional mean of errors assumptions, work as well with conditional expectation's (of the errors (on X))(instead of unconditional ones)? - In order to actually be able to use this result and equal this(i.e. the expectation of the vector of errors) to zero.
Nice job Ben, thanks for posting!
these videos are awesome--thank you so much!
can you suggest books for ANOVA and ANACOVA???
Ben, thanks for your great channel. I every other time come here to remind myself of something I've learned in grad school. Do you keep a repository of your Matlab codes somewhere? I couldn't find them in your website.
very clear congratulations
Why is in every proof I found always Dy the "extra bit" and not just D?
It's just a consequence of the "Linear" assumption in BLUE, i.e. if the model is linear in parameters, it means that the estimator is a linear combination of y's. So any other estimator would have to also be a linear combination of y's, say VY - and you could separate it to the OLS estimator + something else, i.e. (Beta + D)Y = Beta*Y + DY.
Is there a Text book that will help complement this video. It will also be great if you mention the text you might have referred to prepare this video. Thank you.
D is arbitrary as told here. Can we know a little more about 'D' mentioned in the video or is it sufficient to mention that D is an arbitrary matrix of specific size.
Hi, I would recommend either Greene's book or Wooldridge's books here I should think. Probably more Greene if you are looking to understand the matrix workings of econometrics. Best, Ben
Yes, that helped! Thank you!
Why you use "... + D*y" ? Is this then generally valid and why ?
Why not multiply or use a completely different estimator ?