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5h
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.
6h
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.
18h
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.
2d
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.
2d
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
May
1
comment why not handle box-constraints with a transformation
Hi Apurv: Thanks for your reply. Unfortunately, I don't follow it because for the problem I described, lagrange multipliers ( i.e: $\lambda$ ) are not involved.
Apr
23
comment intuition behind subspace of $R^n$
@Blind: Hi: I can email you the page from Byrne's text that has the statements of the two theorems and their proofs. Or I can also latex it in another thread if you want them that way. Thanks and no rush.
Apr
23
comment intuition behind subspace of $R^n$
@Blind: Hi. Although I checked the answer, I went back to my text and the author has something slightly different than you. He has the same theorem as you wrote for the subspace ( the one you titled: projection onto a halfspace but that's probably a typo ) but he claims that it holds for a linear manifold rather than a subspace. Note that the author also has a seperate but related theorem for the case of subspace. The result is the same as the one that you wrote for the subspace except that he has $y$ instead of $y - P_{c}(x)$ in the second term. ???? Thanks for any clarification on this.
Apr
22
comment intuition behind subspace of $R^n$
@Blind: Thank you. That was great. I followed every step and the definitions are now in sync with what Charles Byrne has in his book. Now, I can go back to it and continue reading and wait for confusion to come. When it does, I will write again to this list. It's amazing. Thanks again.
Apr
22
accepted intuition behind subspace of $R^n$
Apr
20
comment intuition behind subspace of $R^n$
Previous should have read : " A subset S of $R^{n}$". Sorry for confusion.
Apr
20
comment intuition behind subspace of $R^n$
I have to leave now but here is how subspace is defined in "A First Course In Optimization:": A subset of $R^{n}$ is a subspace is for every x and y in S and scalars $\alpha$ and $\beta $, the linear combination $\alpha * x + \beta * y $ again belongs to S. But that sounds similar to your linear manifold definition. Thanks.
Apr
20
comment intuition behind subspace of $R^n$
In Prop 2, I don't see "Hence, M is a subspace". I stopped there and will try to understand Prop 3 later. Thanks for any clearing my "denseness". P.S: The way Byrne's defines subspace looks quite similar to how you define linear manifold. I'll fight through both and try to connect the dots.