Survey Methodology
Comparison of some positive variance estimators for the Fay-Herriot small area model

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by Susana Rubin-Bleuer and Yong YouNote 1

  • Release date: June 22, 2016
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Abstract

The restricted maximum likelihood (REML) method is generally used to estimate the variance of the random area effect under the Fay-Herriot model (Fay and Herriot 1979) to obtain the empirical best linear unbiased (EBLUP) estimator of a small area mean. When the REML estimate is zero, the weight of the direct sample estimator is zero and the EBLUP becomes a synthetic estimator. This is not often desirable. As a solution to this problem, Li and Lahiri (2011) and Yoshimori and Lahiri (2014) developed adjusted maximum likelihood (ADM) consistent variance estimators which always yield positive variance estimates. Some of the ADM estimators always yield positive estimates but they have a large bias and this affects the estimation of the mean squared error (MSE) of the EBLUP. We propose to use a MIX variance estimator, defined as a combination of the REML and ADM methods. We show that it is unbiased up to the second order and it always yields a positive variance estimate. Furthermore, we propose an MSE estimator under the MIX method and show via a model-based simulation that in many situations, it performs better than other ‘Taylor linearization’ MSE estimators proposed recently.

Key Words: Variance estimation; Adjusted maximum likelihood; REML; Order of bias; MSE estimation.

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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, 2016

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

Catalogue No. 12-001-X

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