Survey Methodology
With-replacement bootstrap variance estimation for household surveys Principles, examples and implementation

by Pascal Bessonneau, Gwennaëlle Brilhaut, Guillaume Chauvet and Cédric GarciaNote 1

  • Release date: January 6, 2022
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Abstract

Variance estimation is a challenging problem in surveys because there are several nontrivial factors contributing to the total survey error, including sampling and unit non-response. Initially devised to capture the variance of non-trivial statistics based on independent and identically distributed data, the bootstrap method has since been adapted in various ways to address survey-specific elements/factors. In this paper we look into one of those variants, the with-replacement bootstrap. We consider household surveys, with or without sub-sampling of individuals. We make explicit the benchmark variance estimators that the with-replacement bootstrap aims at reproducing. We explain how the bootstrap can be used to account for the impact sampling, treatment of non-response and calibration have on total survey error. For clarity, the proposed methods are illustrated on a running example. They are evaluated through a simulation study, and applied to a French Panel for Urban Policy. Two SAS macros to perform the bootstrap methods are also developed.

Key Words:   Bootstrap; Calibration; Variance estimation; Unit non-response.

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How to cite

Bessonneau, P., Brilhaut, G., Chauvet, G. and Garcia, C. (2021). With-replacement bootstrap variance estimation for household surveys Principles, examples and implementation. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 47, No. 2. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2021002/article/00005-eng.htm.

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ISSN : 1492-0921

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Survey Methodology publishes articles dealing with various aspects of statistical development relevant to a statistical agency, such as design issues in the context of practical constraints, use of different data sources and collection techniques, total survey error, survey evaluation, research in survey methodology, time series analysis, seasonal adjustment, demographic studies, data integration, estimation and data analysis methods, and general survey systems development. The emphasis is placed on the development and evaluation of specific methodologies as applied to data collection or the data themselves. All papers will be refereed. However, the authors retain full responsibility for the contents of their papers and opinions expressed are not necessarily those of the Editorial Board or of Statistics Canada.

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Published by authority of the Minister responsible for Statistics Canada.

© His Majesty the King in Right of Canada as represented by the Minister of Industry, 2022

Use of this publication is governed by the Statistics Canada Open Licence Agreement.

Catalogue No. 12-001-X

Frequency: Semi-annual

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Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. Notation and estimation
Section 3. Bootstrap variance estimation
Section 4. Simulation study
Section 5. Application to the French panel for urban policy
Section 6. Conclusion and future work
Acknowledgements
Appendix
References

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