Hi all,
I'm intersted in draw confidence regions for two estimates that *are not* in
the same GLM, but I know their point estimates c(a,b) and their covariance
matrix V, say. Of course> V[1,2]==V[2,1]
[1] TRUE
Their joint distribution is not binormal (at least i don't know it), but I
know (or I assume) their limiting distribution is Normal, so I can use the
bivariate Wald statistics to get confidence regions. Using ellipse it is
plot(ellipse(V, centre=c(a,b))) #it works
However there are two issues:
I change just one covariance in V, i.e.> V[1,2]==V[2,1]
[1] FALSE
This make no-sense, but
plot(ellipse(V, centre=c(a,b))) #still it works !!!
Am I missing anything?
Furthermore in the help file on ellipse.default() there is written:
"x should be a correlation between -1 and 1 or a square positive definite
matrix at least 2x2 in size. It will be treated as the correlation or
covariance of a multivariate normal distribution"
Mhmm....As far as I know if two r.v. have Gaussian distribution this doesn't
imply that their bivariate distribution is also Gaussian, but however I can
use the bivariate Wald statistics with chi-square distribution with 2 df.
Therefore just one of the followings holds:
1) I can't use plot(ellipse(V, centre=c(a,b))) to estimate Wald -based
confidence regions,
2) the help file is a bit confusing,
3)I'm wronging everything! ;-)
Is there anyone that can give me any advice?
Many thanks,
best,
vito
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