st: Jackknife with clustered survey data

["James Shaw" <ximon1@hotmail.com>]

I have a question about variance estimation with survey data.  The -svr- 
commands in Stata can be used to analyze complex survey data with 
replication methods such as the jackknife.  I am working with a multi-stage 
sample of the US population.  The first-stage sampling was performed without 
replacement (WOR).  Since the sampling fraction was small (<10%), I should 
be able to analyze the data as though sampled with replacement (WR).  The 
first stage units were also selected with unequal probabilites using a 
probability proportional to size (PPS) algorithm.  The second-stage units 
(survey respondents) were selected randomly, and there is no stratification.

I have read (in the manual for SUDAAN) that the jackknife variance estimator 
is applicable when:

(1) WR sampling is used at the first stage or the sampling fraction is small 
in every first-stage stratum.
(2) WR or WOR sampling is used at subsequent stages.
(3) Sampling is performed with equal or unequal probabilities of selection 
at both the first and subsequent stages.

I thought that the jackknife assumes WR sampling AND equal probabilities of 
selection.  Can anyone tell me why the jackknife would still be applicable 
when the first stage sampling was done using PPS (with unequal selection 
probabilities in a single first-stage stratum)?  Thanks!

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