[R] pure statistical question

MUGGEO VITO segramm.pg.lecce at giustizia.it
Fri Dec 21 13:55:26 CET 2001

Dear all,
This is a pure statistical question, not necessarly related to R.
I could not find it in literature.

Suppose I'm intersted in a parameter rho, say, equal to:
where beta1 and beta2 come from a linear model y=beta0+beta1X1+beta2X2+....
Fitting the model I can get the (biased) estimate of r=b1/b2, where b1 and
b2 are the estimates in the regression model; I can get the unbiased
estimate of rho as well as its SE using the delta method.
I'm interested in confidence interval for r.
A simple method could be (I suppose) the classical one, i.e. using the
standard gaussian quantiles: r +/- 1.96*SE.
However because the ratio of two independent normal distribution is a Chaucy
distribution I was thinking about an "exact methods". But the Chaucy
distribution has not mean!!!
My question is
1)If b1 and b2 are independent (X1 and X2 orthogonal) which is the sense of
r and SE if the Chaucy distribution has not moments?
2) b1 and b2 are normal but not independent, their exact distribution is
even Chaucy?
3)After all, is it correct use gaussian quantiles: r +/- 1.96*SE (as n goes
inf, of course)

hope to have been clear, hope in some your advice
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