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Empirical Best Prediction for Small Area Inference with Binary Data

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Abstract

The paper introduces a frequentist's alternative to the recently developed hierarchical Bayes methods for small area estimation with binary data. Specifically, the best predictor (BP) and empirical best predictor (EBP) of small area specific random effect are developed in the context of a mixed logistic model and different asymptotic properties of the proposed BP and EBP are studied. An approximation to the mean squared error (MSE) of the proposed EBP correct up to the order o(m −1) is obtained, where m denotes the number of small areas. The asymptotic behavior of the relative savings loss (RSL) demonstrates the superiority of the proposed EBP over the usual small area proportion.

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Authors and Affiliations

  1. Department of Statistics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH, 44106-7054, USA

    Jiming Jiang

  2. Department of Mathematics and Statistics, University of Nebraska at Lincoln, Lincoln, NE, 68588-0323, USA

    P. Lahiri

Authors
  1. Jiming Jiang
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  2. P. Lahiri
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Jiang, J., Lahiri, P. Empirical Best Prediction for Small Area Inference with Binary Data. Annals of the Institute of Statistical Mathematics 53, 217–243 (2001). https://doi.org/10.1023/A:1012410420337

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  • DOI: https://doi.org/10.1023/A:1012410420337

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