Empirical best prediction under area-level Poisson mixed models

Miguel Boubeta (), María José Lombardía () and Domingo Morales ()
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Miguel Boubeta: Universidade da Coruña
María José Lombardía: Universidade da Coruña
Domingo Morales: Universidad Miguel Hernández de Elche

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2016, vol. 25, issue 3, No 8, 548-569

Abstract: Abstract The paper studies the applicability of area-level Poisson mixed models to estimate small area counting indicators. Among the available procedures for fitting generalized linear models, the method of moments (MM) and the penalised quasi-likelihood (PQL) method are employed. The empirical best predictor (EBP) of the area mean is derived using MM and compared with plug-in alternatives using MM and PQL. The plug-in estimator using PQL is computationally faster and provides competitive performance with respect to EBP that involves high complex integrals. An approximation to the mean squared error (MSE) of the EBP is given and three MSE estimators are proposed. The first two MSE estimators are plug-in estimators without and with bias correction to the second order and the third one is based on parametric bootstrap. Several simulation experiments are carried out for analysing the behaviour of the EBP and for comparing the estimators of the MSE of the EBP. A good choice in practice is the bootstrap alternative since it performs similarly to the analytical versions and is computationally faster. The developed methodology and software are applied to data from the 2008 Spanish living condition survey. The target of the application is the estimation of poverty rates at province level.

Keywords: Bootstrap; Empirical best predictor; Mean squared error; Method of moments; Poisson mixed models; Poverty; 62J12 Generalized linear models; 62P25 Applications to social sciences; 62D05 Sampling theory; sample surveys (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (17)

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DOI: 10.1007/s11749-015-0469-8

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