Survey Methodology
Small area estimation methods under cut-off sampling

by María Guadarrama, Isabel Molina and Yves TilléNote 1

  • Release date: June 30, 2020
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Abstract

Cut-off sampling is applied when there is a subset of units from the population from which getting the required information is too expensive or difficult and, therefore, those units are deliberately excluded from sample selection. If those excluded units are different from the sampled ones in the characteristics of interest, naïve estimators may be severely biased. Calibration estimators have been proposed to reduce the design-bias. However, when estimating in small domains, they can be inefficient even in the absence of cut-off sampling. Model-based small area estimation methods may prove useful for reducing the bias due to cut-off sampling if the assumed model holds for the whole population. At the same time, for small domains, these methods provide more efficient estimators than calibration methods. Since model-based properties are obtained assuming that the model holds but no model is exactly true, here we analyze the design properties of calibration and model-based procedures for estimation of small domain characteristics under cut-off sampling. Our results confirm that model-based estimators reduce the bias due to cut-off sampling and perform significantly better in terms of design mean squared error.

Key Words:        Calibration estimators; Cut-off sampling; Empirical best linear unbiased predictor (EBLUP); Empirical best/Bayes predictor (EBP); Nested-error model; Unit level models.

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How to cite

Guadarrama, M., Molina, I. and Tillé, Y.  (2020). Small area estimation methods under cut-off sampling. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 46, No. 1. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2020001/article/00004-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, 2020

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. Cut-off sampling in small domains
Section 3. Basic direct estimators
Section 4. Calibration estimators
Section 5. EBLUP under the nested error model
Section 6. Empirical best predictor under the nested error model
Section 7. MSE estimation
Section 8. Simulation experiments
Section 9. Estimation of total sales in Spanish provinces
Section 10. Conclusions
Acknowledgements
Appendix
References

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