Survey Methodology
Variance estimation in multi-phase calibration

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by Noam Cohen, Dan Ben-Hur and Luisa BurckNote 1

  • Release date: June 22, 2017
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Abstract

The derivation of estimators in a multi-phase calibration process requires a sequential computation of estimators and calibrated weights of previous phases in order to obtain those of later ones. Already after two phases of calibration the estimators and their variances involve calibration factors from both phases and the formulae become cumbersome and uninformative. As a consequence the literature so far deals mainly with two phases while three phases or more are rarely being considered. The analysis in some cases is ad-hoc for a specific design and no comprehensive methodology for constructing calibrated estimators, and more challengingly, estimating their variances in three or more phases was formed. We provide a closed form formula for the variance of multi-phase calibrated estimators that holds for any number of phases. By specifying a new presentation of multi-phase calibrated weights it is possible to construct calibrated estimators that have the form of multi-variate regression estimators which enables a computation of a consistent estimator for their variance. This new variance estimator is not only general for any number of phases but also has some favorable characteristics. A comparison to other estimators in the special case of two-phase calibration and another independent study for three phases are presented.

Key Words: Calibration; Multi-phase sampling; Generalized regression.

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How to cite

Cohen, N., Ben-Hur, D. and Burck, L. (2017). Variance estimation in multi-phase calibration. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 43, No. 1. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2017001/article/14823-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.

© Minister of Industry, 2017

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
Section 3. Calibration with GLS distance
Section 4. A simulation study
Section 5. Concluding remarks
Appendix A
Appendix B
References

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