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Small area estimation using skew normal models

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  • Ferraz, V.R.S.
  • Moura, F.A.S.

Abstract

Two connected extensions of the Fay–Herriot small area level model that are of practical and theoretical interest are proposed. The first extension allows for the sampling error to be non-symmetrically distributed. This is important for cases in which the sample sizes in the areas are not large enough to rely on the central limit theorem (CLT). This is dealt with by assuming that the sample error is skew normally distributed. The second extension proposes to jointly model the direct survey estimator and its respective variance estimator, borrowing strength from all areas. In this way, all sources of uncertainties are taken into account. The proposed model has been applied to a real data set and compared with the usual Fay–Herriot model under the assumption of unknown sampling variances. A simulation study was carried out to evaluate the frequentist properties of the proposed model. The evaluation studies show that the proposed model is more efficient for small area predictions under skewed data than the customarily employed normal area model.

Suggested Citation

  • Ferraz, V.R.S. & Moura, F.A.S., 2012. "Small area estimation using skew normal models," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2864-2874.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:10:p:2864-2874
    DOI: 10.1016/j.csda.2011.07.005
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    References listed on IDEAS

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    1. Abanto-Valle, C.A. & Bandyopadhyay, D. & Lachos, V.H. & Enriquez, I., 2010. "Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2883-2898, December.
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    3. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    4. R. A. Sugden & T. M. F. Smith & R. P. Jones, 2000. "Cochran's rule for simple random sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 787-793.
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    Cited by:

    1. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Fernando A. S. Moura & André Felipe Neves & Denise Britz do N. Silva, 2017. "Small area models for skewed Brazilian business survey data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1039-1055, October.
    3. Azevedo Neves André Felipe & Nascimento Silva Denise Britz do & Silva Moura Fernando Antônio da, 2020. "Skew normal small area time models for the Brazilian annual service sector survey," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 84-102, August.
    4. Liseo, Brunero & Parisi, Antonio, 2013. "Bayesian inference for the multivariate skew-normal model: A population Monte Carlo approach," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 125-138.
    5. Alexander, Carol & Meng, Xiaochun & Wei, Wei, 2022. "Targeting Kollo skewness with random orthogonal matrix simulation," European Journal of Operational Research, Elsevier, vol. 299(1), pages 362-376.
    6. André Felipe Azevedo Neves & Denise Britz do Nascimento Silva & Fernando Antônio da Silva Moura, 2020. "Skew normal small area time models for the Brazilian annual service sector survey," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 84-102, August.

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