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Re: st: Jackknife with clustered survey data

From   "James Shaw" <>
Subject   Re: st: Jackknife with clustered survey data
Date   Sun, 25 Mar 2007 08:28:47 -0400

Thank you for your response. I will take a look at the papers you suggested. I have read several papers discussing variants of the jackknife designed for handling WOR sampling and/or unequal selection probabilities. Most notably:

Berger YG, Skinner CJ. A jackknife variance estimator for unequal probability sampling. J R Statist Soc B 2005; 67(Part 1): 79-89.

In general, these suggest that the jackknife as implemented in Stata's -svr- commands and SUDAAN is not appropriate for all multistsage sampling designs. In fact, my concern is that the jackknife is only applicable with equal selection probabilities at the first stage or with stratified data where the probability of selection may vary across strata but is constant among PSUs within each stratum. Since the data I am working with are not stratified, this presents a problem.

One further question. If the jackknife were appropriate for use with unequal probability sampling at the first stage, then would this not imply that the bootstrap could be used instead? I assume that the sampling weights would need to be suitably rescaled for each replicate sample.

From: "Stas Kolenikov" <>
Subject: Re: st: Jackknife with clustered survey data
Date: Sat, 24 Mar 2007 14:42:54 -0500

If you are interested in technical details, you should check Krewski &
Rao and Rao & Wu original papers:,, or Shao's review: The way I am
thinking about the resampling methods, and jackknife especially, is
that they are taking small steps around the maximum of the likelihood,
trying to get a feel of the surface around that max, and then it does
not matter much whether the weights/unequal prob of selection are used
or not: it would change the structure of those small steps, but won't
change things conceptually.

On 3/24/07, James Shaw <> wrote:
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!

Stas Kolenikov
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