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 Mar 21 asked is there a closed form solution for the following relationship Feb 29 comment why does this simple function converge to f(x) pointwise thanks so much ian. I think I get it now. I appreciate your patience and help. Feb 28 comment why does this simple function converge to f(x) pointwise Hi All: I read the explanations and I understand copper.hat's equivalent function but I think I'm missing something. $f(x)$ returns a value of $y$ for a given $x$. So how could a function $f_{n}$ which is composed of indicator functions ever approach $f$ since it's returning $1 \times j \times 2^{-n}$ whenever the set satisfies that condition of the indicator function. thanks. Feb 28 comment why does this simple function converge to f(x) pointwise thanks. what both of you said sounds very clear I have to print out read it very carefully to see if I "get it". but if anyone knows of a picture that describes what is going on, that would probably help me a lot. all the best and thank you very much copper.hat and ian. Feb 28 accepted why does this simple function converge to f(x) pointwise Feb 28 asked why does this simple function converge to f(x) pointwise 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.