Biometrika Advance Access originally published online on April 7, 2009
Biometrika 2009 96(2):457-468; doi:10.1093/biomet/asp003
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Article |
Jackknife estimation of mean squared error of small area predictors in nonlinear mixed models
Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287-1804, U.S.A. sharon.lohr{at}asu.edu
School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada jrao{at}math.carleton.ca
Received for publication 1 October 2007.
Revision received 1 August 2008.
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Abstract |
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Empirical Bayes predictors of small area parameters of interest are often obtained under a linear mixed model for continuous response data or a generalized linear mixed model for binary responses or count data. However, estimation of the unconditional mean squared error of prediction is complicated, particularly for a nonlinear mixed model. Jiang et al. (2002) proposed a jackknife method for estimating the unconditional mean squared error and showed that the resulting estimator is nearly unbiased. The leading term of this estimator does not depend on the area-specific responses in the nonlinear case, whereas the posterior variance of the small area parameter given the model parameters is area-specific. Rao (2003) proposed an alternative method that leads to a computationally simpler jackknife estimator with an area-specific leading term. We show that a modification of Rao's method leads to a nearly unbiased area-specific jackknife estimator, which is also nearly unbiased for the conditional mean squared error given the area-specific responses. We examine the relative performances of the jackknife estimators, conditionally as well as unconditionally, in a simulation study, and apply the proposed method to estimate small area mean squared errors in disease mapping problems.
Key Words: Area-specific • Beta-binomial model • Binary response • Disease mapping • Empirical Bayes • Generalized linear mixed model