Bernoulli

  • Bernoulli
  • Volume 18, Number 4 (2012), 1320-1340.

On a characterization of ordered pivotal sampling

Guillaume Chauvet

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Abstract

When auxiliary information is available at the design stage, samples may be selected by means of balanced sampling. Deville and Tillé proposed in 2004 a general algorithm to perform balanced sampling, named the cube method. In this paper, we are interested in a particular case of the cube method named pivotal sampling, and first described by Deville and Tillé in 1998. We show that this sampling algorithm, when applied to units ranked in a fixed order, is equivalent to Deville’s systematic sampling, in the sense that both algorithms lead to the same sampling design. This characterization enables the computation of the second-order inclusion probabilities for pivotal sampling. We show that the pivotal sampling enables to take account of an appropriate ordering of the units to achieve a variance reduction, while limiting the loss of efficiency if the ordering is not appropriate.

Article information

Source
Bernoulli, Volume 18, Number 4 (2012), 1320-1340.

Dates
First available in Project Euclid: 12 November 2012

Permanent link to this document
https://projecteuclid.org/euclid.bj/1352727813

Digital Object Identifier
doi:10.3150/11-BEJ380

Mathematical Reviews number (MathSciNet)
MR2995798

Zentralblatt MATH identifier
1329.62054

Keywords
balanced sampling cube method design effect sampling algorithm second order inclusion probabilities unequal probabilities

Citation

Chauvet, Guillaume. On a characterization of ordered pivotal sampling. Bernoulli 18 (2012), no. 4, 1320--1340. doi:10.3150/11-BEJ380. https://projecteuclid.org/euclid.bj/1352727813


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