Survey Methodology
On combining independent probability samples

by Anton Grafström, Magnus Ekström, Bengt Gunnar Jonsson, Per-Anders Esseen and Göran StåhlNote 1

  • Release date: June 27, 2019
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Abstract

Merging available sources of information is becoming increasingly important for improving estimates of population characteristics in a variety of fields. In presence of several independent probability samples from a finite population we investigate options for a combined estimator of the population total, based on either a linear combination of the separate estimators or on the combined sample approach. A linear combination estimator based on estimated variances can be biased as the separate estimators of the population total can be highly correlated to their respective variance estimators. We illustrate the possibility to use the combined sample to estimate the variances of the separate estimators, which results in general pooled variance estimators. These pooled variance estimators use all available information and have potential to significantly reduce bias of a linear combination of separate estimators.

Key Words:      Horvitz-Thompson estimator; Inclusion probabilities; Linear combination estimator; Variance estimation.

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How to cite

Grafström, A., Ekström, M., Jonsson, B.G., Esseen, P.-A. and Ståhl, G. (2019). On combining independent probability samples. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 45, No. 2. Paper available at https://www150.statcan.gc.ca/n1/pub/12-001-x/2019002/article/00003-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.

© Her Majesty the Queen in Right of Canada as represented by the Minister of Industry, 2019

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

Catalogue No. 12-001-X

Frequency: Semi-annual

Ottawa

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Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. Combining separate estimates
Section 3. Combining samples
Section 4. Simulation examples
Section 5. Discussion
Acknowledgements
References

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