Survey Methodology
Replication variance estimation after sample-based calibration

by Jean D. Opsomer and Andreea L. ErciulescuNote 1

  • Release date: January 6, 2022
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Abstract

Sample-based calibration occurs when the weights of a survey are calibrated to control totals that are random, instead of representing fixed population-level totals. Control totals may be estimated from different phases of the same survey or from another survey. Under sample-based calibration, valid variance estimation requires that the error contribution due to estimating the control totals be accounted for. We propose a new variance estimation method that directly uses the replicate weights from two surveys, one survey being used to provide control totals for calibration of the other survey weights. No restrictions are set on the nature of the two replication methods and no variance-covariance estimates need to be computed, making the proposed method straightforward to implement in practice. A general description of the method for surveys with two arbitrary replication methods with different numbers of replicates is provided. It is shown that the resulting variance estimator is consistent for the asymptotic variance of the calibrated estimator, when calibration is done using regression estimation or raking. The method is illustrated in a real-world application, in which the demographic composition of two surveys needs to be harmonized to improve the comparability of the survey estimates.

Key Words:   Fishing; Hunting and wildlife watching surveys; Raking; Regression estimation; Replicate construction.

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How to cite

Opsomer, J.D., and Erciulescu, A.L. (2021). Replication variance estimation after sample-based calibration. 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/00006-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. Sample-based regression calibration
Section 3. Sample-based raking calibration
Section 4. Application
Section 5. Conclusions
References

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