its not the symmetry in that line, its the fact that in matrix
expressions, you can move scalars wherever you like, such as out front
(i.e., to the left). that leaves the middle easy to deal with.
Gary
On Wed, 29 Sep 2004, Kentaro Fukumoto wrote:
Hi Gov. 2001 folks,
Olivia, thank you for quick response.
No. You should estimate sigma^2 according to the
equation from
the section hand out. You cannot use the sd() function to
calculate sigma.
I didn't know sd function.
But, in order to compute 95% quantile of normal distribution,
we should get standard error, even if we don't name it such?
I read
Rice's p. 538.
But I can't understand, in the proof of theorem B,
how he uses symmetry of X'X and XX'.
Z <- matrix(1:12, nrow = 2, ncol
= 6)
t(Z) %*% Z # Note that entry (i,j) is the same as entry (j,i)
for all i and j.
Z %*% t(Z) # Also symmetric!
I knew that.
My question is how he takes advantage of symmetry of X'X and XX'
in deriving sigma^2(X'X)^-1 from (X'X)^-1 X'SIGMAeeX(X'X)^-1
Kentaro
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