GLS estimators in matrix form - part 2

This video explains how to derive GLS estimators in matrix form.
Check out oxbridge-tutor.... for course materials, and information regarding updates on each of the courses. 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....

[@user-xh2vb5iq8d]

Thank you so much

[@jairjuliocc]

This videos are really good, maybe in the future you can put the implementation in a programming language like python or C. Thanks

[@anubismva]

Very good explanation!

[@mariogonzalezsauri4632]

Dear Ben, can you elaborate a bit more about the assumptions behind the symmetry of P?

[@hongsheny67]

I think as there are more than one possible solution when calculating P, just use the P that derive from symmetric would be easier

[@kottelkannim4919]

I hope I am not misleading you.
Example:
[1 0 [ 2 0 [ 0.25 0 [ 2 0
0 1] = 0 5 ] 0 0.04 ] 0 5 ]
Alternatively,
[0.25 0 [ 0.5 0 [ 1 0 [ 0.5 0
0 0.04 ] = 0 0.2 ] 0 1 ] 0 0.2 ]
Assumptions for this matrix factorization:
1. OMEGA matrix is diagonal
2. OMEGA's (diagonal) elements are nonnegative. This is true since it is a real valued covariance matrix.

[@liyangwu5395]

Could u explain why the p is symmetric, can we prove that?

[@carvallocesar]

the multiplication of 2 matrices is P^2 of if P*P' ?

[@SpartacanUsuals]

Hi Cesar, the multiplication of two matrices is P^2 only if both matrices are the same. In your example, if P = P'. Hope that helps, Best, Ben

[@zhizhongpu8937]

To clarify confusion, it's not necessary to assume that P is symmetric in order to derive the GLS estimator. See ruclips.net/video/ZFQDn84fuJI/видео.html

[@kottelkannim4919]

It maybe answered later on in the course, but how exactly one estimates OMEGA matrix in the first place?