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I know I am supposed to start from

$N^{1/2}[N^{-1}\sum x_{i}u_{i}]$

Then by central limit theorem that that it is asymptotically

$ N(E(x_{i}u_{i}),var(x_{i}u_{i})) $

and $E(x_{i}u_{i})=0$

so $ N(0,var(x_{i}u_{i})) $

from there I cant see how I get to the correct result which is supposed to be

$N(0,(E(x_{i}x'_{i}))^{-1}E(u^2_{i}x_{i}x'_{i})(E(x_{i}x'_{i}))^{-1})$

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  • $\begingroup$ it looks like you have OLS with heteroskedastic error term so check out the well known paper by Halbert White whose title currently escapes me. I'll see if I can find the name of it. $\endgroup$ – mlofton Dec 20 '18 at 16:25
  • $\begingroup$ The derivation is probably in here. pdfs.semanticscholar.org/f9cc/… $\endgroup$ – mlofton Dec 20 '18 at 16:26
  • $\begingroup$ Here's another link that can probably lead to some good references. en.wikipedia.org/wiki/… $\endgroup$ – mlofton Dec 20 '18 at 16:30

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