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Aug
18
revised how to project optimal parameters on to feasible region
edited tags
Aug
18
asked how to project optimal parameters on to feasible region
Aug
2
comment not understanding a step in a proof
I followed both of the explanations. Thanks again to both of you.
Aug
2
accepted not understanding a step in a proof
Aug
1
comment not understanding a step in a proof
both of you have answered so what am I supposed to do if I understand both explanations. which one do I check ? thanks.
Aug
1
comment not understanding a step in a proof
I will print out, read carefully, make sure I understand it and then check it. Thank you very much for your thorough explanation. It's really appreciated.
Aug
1
asked not understanding a step in a proof
Jul
30
comment Central limit theorem in multidimension with unknown covariance
That's a really nice book that doesn't get enough hype. And since White passed away, it will probably now get even less. IMHO, if you have hamilton's text and white's text, you pretty much have the whole "kit and caboodle" in econometric time series. All the best.
Jul
28
comment Help in partial derivative during maximization for estimation problem
Hi again: One more thing. Note that the expression for G will contain the MLE of h so you will need to substitute the expression for the MLE of h into G so that the expression for the MLE of $\sigma^2_w$ is a function involving the things that $\hat{h}$ is composed of. I didn't check the other MLE's so but of course the MLE of $h$ will need to be correct in order for the MLE of $\sigma^2_w$ to be correct.
Jul
28
comment Help in partial derivative during maximization for estimation problem
Hi: Consider Q and call the expression between the square brackets G. Then,taking the derivative of the log likelihood expression Q with respect to $\sigma^2_w$ and setting it to zero, gives $ -\frac{N}{2 \sigma^2_{w}} + \frac{1}{2} \frac{1}{{(\sigma^2_w)}^2}[G] = 0 $. Then, finding the common denominator gives $\frac{-N \sigma^2_w + G}{2(\sigma^2_w)^2} = 0$. Solving that for $\sigma^2_w$ gives $\sigma^2_w = \frac{G}{N}$. Let me know if that makes sense.
Jul
27
comment Central limit theorem in multidimension with unknown covariance
Halbert White's "asymptotic theory for econometricians" should have it. Basically, by slutsky's theorem, if you have a consistent estimator, $\hat{\Sigma}$, then the proof of the estimated case follows the same reasoning. But you're better off checking White's text than having me try to explain it.
Jul
25
comment Help in partial derivative during maximization for estimation problem
I@shristi: I will write the equations no problem but you did the harder part so I know you can do this. Just take the derivative with respect to $\sigma^2_w$ of the two terms that contain $\sigma^2_w$. Don't touch anything else. Then set that equal to zero and solve for $\sigma^2_w$ and you will see that $\hat\sigma^2_w = G/N$. I'm not trying to be annoying. I just know that you'll kick yourself when you see the solution so I'm trying to avoid that scenario. All the best and let me know.
Jul
25
comment Help in partial derivative during maximization for estimation problem
My apologies: By square brackets I mean the square brackets where you say: "The expression for the log likelihood.
Jul
23
comment Help in partial derivative during maximization for estimation problem
@shristi: I don't have time to write it out right now ( you interchanged $\sigma^2_w$ and $\sigma^2_v$ so let's stick with $\sigma^2_w$ ) but I did the derivatives and obtained that $\hat{\sigma}^2_w = \frac{G}{N}$ where $G$ is the expression between the two square brackets. See if you can obtain the same thing and let me know. If you can't, I'll write it out.
Jul
23
comment Help in partial derivative during maximization for estimation problem
@shristi:I apologize for my weird previous email. I was editing my response and then I lost the page and couldn't find it again. I will print out and take a look at the equations but I'm pretty busy at the moment so I may not get back to you so quickly. I will try but hopefully someone else will chime in the meantime. all the best.
Jul
23
revised matching the powers of the coefficients of polynomials
added 466 characters in body
Jul
22
comment Help in partial derivative during maximization for estimation problem
I'm not sure about this but did you make a mistake in te derivation of the likelihood}$. Regarding the second term of Q, I could be totally off here but I don't think the $\sigma^2_w$ term should be on the outside since
Jul
22
revised matching the powers of the coefficients of polynomials
added 10 characters in body
Jul
22
revised matching the powers of the coefficients of polynomials
added 2 characters in body
Jul
22
asked matching the powers of the coefficients of polynomials