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Algorithms to find exact inclusion probabilities for 2P pi ps sampling designs
Örebro University, Swedish Business School at Örebro University.
2011 (English)In: Lithuanian Mathematical Journal, ISSN 0363-1672, E-ISSN 1573-8825, Vol. 51, no 3, p. 425-439Article in journal (Refereed) Published
Abstract [en]

The statistical literature contains several proposals for methods generating fixed-size without-replacement pi ps sampling designs. pi ps designs with fixed size have rarely been used due to difficulties with implementation. Recently, a new method was proposed viz. the 2P pi ps design using a two-phase approach. It was shown that the first-order inclusion probabilities of the 2P pi ps design are asymptotically equal to the target inclusion probabilities of a p pi s design. This paper extends the work on the 2P pi ps design and presents algorithms for calculation of exact first-and second-order inclusion probabilities. Starting from a probability mass function (pmf) of the sum of N independent, but not equally distributed Bernoulli variables, the algorithms are based on derived expressions for the pmfs of sums of N - 1 and N - 2 variables, respectively. Exact inclusion probabilities facilitate standard-based inference and provide a tool for studying the properties of the 2P pi ps design. Furthermore, empirical results presented show that the properties of the suggested point estimator can be improved using a more general 2P pi ps design. In addition, the frequently used Conditional Poisson sampling design is shown to be a special case of this more general 2P pi ps design.

Place, publisher, year, edition, pages
2011. Vol. 51, no 3, p. 425-439
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:oru:diva-18686ISI: 000294475200012OAI: oai:DiVA.org:oru-18686DiVA, id: diva2:444671
Available from: 2011-09-29 Created: 2011-09-29 Last updated: 2017-12-08Bibliographically approved

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Olofsson, Jens

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CiteExportLink to record
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  • apa
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  • de-DE
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  • nn-NB
  • sv-SE
  • Other locale
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  • asciidoc
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