st: Variance of ratio estimator

[Marcello Pagano <pagano@hsph.harvard.edu>]

Balduccio Attacchini would like to know:

I’d like to know the formula adopted by Stata in calculating the
variance estimator for ratio estimator in stratified single–stage design 
and with a finite population correction.
In particular, when I set
svyset_n, strata(..) fpc(..)
and then I run
svy: ratio y_total/x_total
The command returns an information labelled as 'Linearized Std. Err.'
The formula showed in page 263 of Survey data-Release 9(Stata) does not 
solve my question.
However the manual does not allow the case for Stratified single-stage 
design and Finite population correction (even the link to pag 259 is 
unclear being referred only to the variance estimation of a total).
So what is the formula behind the Linearized STd. Err. returned by the 
following commands?:
svyset _n, strata(..) fpc(..)
svy: ratio y_total/x_total

Thanks,
Balduccio
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