Copula-based predictions in small area estimation |
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Authors: | Kanika Grover Elif F Acar Mahmoud Torabi |
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Institution: | 1. Census Operations Division, Statistics Canada, 170 Tunney's Pasture Driveway, Ottawa, Ontario, Canada, K1A 0T6;2. Department of Statistics, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2 |
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Abstract: | Unit-level regression models are commonly used in small area estimation (SAE) to obtain an empirical best linear unbiased prediction of small area characteristics. The underlying assumptions of these models, however, may be unrealistic in some applications. Previous work developed a copula-based SAE model where the empirical Kendall's tau was used to estimate the dependence between two units from the same area. In this article, we propose a likelihood framework to estimate the intra-class dependence of the multivariate exchangeable copula for the empirical best unbiased prediction (EBUP) of small area means. One appeal of the proposed approach lies in its accommodation of both parametric and semi-parametric estimation approaches. Under each estimation method, we further propose a bootstrap approach to obtain a nearly unbiased estimator of the mean squared prediction error of the EBUP of small area means. The performance of the proposed methods is evaluated through simulation studies and also by a real data application. |
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Keywords: | Best unbiased predictor bootstrap multivariate exchangeable copula pseudo-copula likelihood small area estimation |
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