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Analytic and bootstrap approximations of prediction errors under a multivariate fay-herriot model


  • González Manteiga, Wenceslao
  • Lombardía, Maria J.
  • Molina, Isabel
  • Morales, Domingo
  • Santamaría, Laureano


A Multivariate Fay-Herriot model is used to aid the prediction of small area parameters of dependent variables with sample data aggregated to area level. The empirical best linear unbiased predictor of the parameter vector is used, and an approximation of the elements of the mean cross product error matrix is obtained by an extension of the results of Prasad and Rao (1990) to the multiparameter case. Three different bootstrap approximations of those elements are introduced, and a simulation study is developed in order to compare the efficiency of all presented approximations, including a comparison under lack of normality. Further, the number of replications needed for the bootstrap procedures to get stabilized are studied.

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  • González Manteiga, Wenceslao & Lombardía, Maria J. & Molina, Isabel & Morales, Domingo & Santamaría, Laureano, 2005. "Analytic and bootstrap approximations of prediction errors under a multivariate fay-herriot model," DES - Working Papers. Statistics and Econometrics. WS ws054910, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:ws054910

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    References listed on IDEAS

    1. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
    2. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew "t"-distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389.
    3. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 19-40, Suppl. De.
    4. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
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