Survey Methodology
Two local diagnostics to evaluate the efficiency of the empirical best predictor under the Fay-Herriot model

by Éric Lesage, Jean-François Beaumont and Cynthia BocciNote 1

  • Release date: January 6, 2022
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Abstract

The Fay-Herriot model is often used to produce small area estimates. These estimates are generally more efficient than standard direct estimates. In order to evaluate the efficiency gains obtained by small area estimation methods, model mean square error estimates are usually produced. However, these estimates do not reflect all the peculiarities of a given domain (or area) because model mean square errors integrate out the local effects. An alternative is to estimate the design mean square error of small area estimators, which is often more attractive from a user point of view. However, it is known that design mean square error estimates can be very unstable, especially for domains with few sampled units. In this paper, we propose two local diagnostics that aim to choose between the empirical best predictor and the direct estimator for a particular domain. We first find an interval for the local effect such that the best predictor is more efficient under the design than the direct estimator. Then, we consider two different approaches to assess whether it is plausible that the local effect falls in this interval. We evaluate our diagnostics using a simulation study. Our preliminary results indicate that our diagnostics are effective for choosing between the empirical best predictor and the direct estimator.

Key Words: Empirical best predictor; Design mean square error; Model mean square error; Local diagnostic; Local effect; Fay-Herriot model.

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How to cite

Lesage, É., Beaumont, J.-F. and Bocci, C. (2021). Two local diagnostics to evaluate the efficiency of the empirical best predictor under the Fay-Herriot model. 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/00001-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

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Catalogue No. 12-001-X

Frequency: Semi-annual

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Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. The Fay-Herriot model and the best predictor
Section 3. The mean square errors of the direct and B estimators
Section 4. Two diagnostics to evaluate the local performance of the B estimator
Section 5. Empirical version of the B estimator and diagnostics
Section 6. Simulation study
Section 7. Conclusion
Appendix
References

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