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On the non-recursive implementation of multistage sampling without replacement.

Philippe Aubry1

  • 1OFB - Office français de la biodiversité - Direction surveillance, évaluation, données - Unité données et appui méthodologique, Saint Benoist, BP 20, F-78612 Le Perray-en-Yvelines, France.

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Summary
This summary is machine-generated.

Estimating variance in multistage sampling without replacement is computationally intensive. This study presents a general, efficient iterative method using recurrence relations for accurate variance estimation in complex sampling designs.

Keywords:
Approximate variance estimatorArray data structuresExpansion estimatorHorvitz-Thompson estimatorMultistage samplingNon-recursive algorithmsSelf-weighted designSen-Yates-Grundy variance

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Area of Science:

  • Statistics
  • Survey Methodology

Background:

  • Variance estimation in multistage sampling without replacement is computationally demanding.
  • Existing methods become complex and difficult to implement beyond two sampling stages.

Purpose of the Study:

  • To develop a general and computationally efficient method for variance estimation in multistage sampling without replacement.
  • To overcome the formulation and implementation challenges of traditional methods for complex sampling designs.

Main Methods:

  • A full-iterative implementation approach is presented.
  • Implicit estimator definitions are translated into iterative algorithms using recurrence relations.
  • The algorithms utilize dense array data structures, optimizing memory usage.

Main Results:

  • The proposed iterative method provides a general solution for variance estimation across any number of sampling stages.
  • The approach is computationally efficient, reducing the burden compared to explicit formula implementations.
  • Memory requirements are minimized as most is used only in preliminary steps.

Conclusions:

  • The presented iterative algorithms offer a practical and efficient solution for variance estimation in multistage sampling.
  • This method simplifies the implementation and computation for complex survey designs.
  • The approach enhances the feasibility of accurate variance estimation in advanced statistical analyses.