Selection of small area estimators
Small area estimators, based on area level models, are likely to achieve high precision when the model is correctly specified. In this point, the question of model selection plays an important role. We talk about estimation selection instead of model selection, in a small area context, as the model is only an artifact to derive the area estimators. In fact, the working model is often simpler than the data-generating model. We propose to perform the selection step using an AIC. When mixed models are among the candidate models, different versions for the penalty term, and either conditional or marginal log-likelihoods, have been considered in the literature. We highlight three Generalized AIC statistics useful in small area problems. The candidate models are derived using different explanatory variables and functional forms relating to the response. Numerical results show the good performance of our proposal, which selects the estimators with the smallest mean squared error.
Palabras clave / Keywords: Akaike information criterion (AIC) bootstrap Fay-Herriot model generalized degree of freedom monotone model spline regression small area estimation
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