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Small area prediction for a unit-level lognormal model

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  • Berg, Emily
  • Chandra, Hukum

Abstract

Many variables of interest in business and agricultural surveys have skewed distributions. Small area estimation methods are investigated under an assumption that the lognormal model is a reasonable approximation for the distribution of the response given covariates. Closed form expressions for an empirical Bayes (EB) predictor and for the associated mean squared error estimator are derived. In simulation studies, the EB predictors are more efficient than model-based direct and synthetic estimators previously proposed for lognormal data. Also, coverage of confidence intervals for the lognormal predictions approximate the nominal coverage. The simulations also demonstrate that the suggested predictor is robust to departures from the assumptions of the lognormal model. The methodology is successfully applied to estimate erosion rates for hydrologic units using data from the Conservation Effects Assessment Project.

Suggested Citation

  • Berg, Emily & Chandra, Hukum, 2014. "Small area prediction for a unit-level lognormal model," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 159-175.
    • Handle: RePEc:eee:csdana:v:78:y:2014:i:c:p:159-175
    DOI: 10.1016/j.csda.2014.03.007
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    References listed on IDEAS

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    Cited by:

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    2. Adam Chwila & Tomasz Żądło, 2020. "On the choice of the number of Monte Carlo iterations and bootstrap replicates in Empirical Best Prediction," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 35-60, June.
    3. J. N. K. Rao, 2015. "Inferential issues in model-based small area estimation: some new developments," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(4), pages 491-510, December.
    4. Dian Handayani & Henk Folmer & Anang Kurnia & Khairil Anwar Notodiputro, 2018. "The spatial empirical Bayes predictor of the small area mean for a lognormal variable of interest and spatially correlated random effects," Empirical Economics, Springer, vol. 55(1), pages 147-167, August.
    5. Zimmermann Thomas & Münnich Ralf Thomas, 2018. "Small Area Estimation with a Lognormal Mixed Model under Informative Sampling," Journal of Official Statistics, Sciendo, vol. 34(2), pages 523-542, June.
    6. Rao J. N. K., 2015. "Inferential Issues in Model-Based Small Area Estimation: Some New Developments," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 491-510, December.
    7. J. N. K. Rao, 2015. "Inferential Issues In Model-Based Small Area Estimation: Some New Developments," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 491-510, December.

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