A Hierarchical Bayes Unit-Level Small Area Estimation Model for Normal Mixture Populations
Gauri Sankar Datta and
Abhyuday Mandal ()
Additional contact information
Shuchi Goyal: University of California at Los Angeles
Gauri Sankar Datta: University of Georgia
Abhyuday Mandal: University of Georgia
Sankhya B: The Indian Journal of Statistics, 2021, vol. 83, issue 1, No 10, 215-241
Abstract National statistical agencies are regularly required to produce estimates about various subpopulations, formed by demographic and/or geographic classifications, based on a limited number of samples. Traditional direct estimates computed using only sampled data from individual subpopulations are usually unreliable due to small sample sizes. Subpopulations with small samples are termed small areas or small domains. To improve on the less reliable direct estimates, model-based estimates, which borrow information from suitable auxiliary variables, have been extensively proposed in the literature. However, standard model-based estimates rely on the normality assumptions of the error terms. In this research we propose a hierarchical Bayesian (HB) method for the unit-level nested error regression model based on a normal mixture for the unit-level error distribution. Our method proposed here is applicable to model cases with unit-level error outliers as well as cases where each small area population is comprised of two subgroups, neither of which can be treated as an outlier. Our proposed method is more robust than the normality based standard HB method (Datta and Ghosh, Annals Stat. 19, 1748–1770, 1991) to handle outliers or multiple subgroups in the population. Our proposal assumes two subgroups and the two-component mixture model that has been recently proposed by Chakraborty et al. (Int. Stat. Rev. 87, 158–176, 2019) to address outliers. To implement our proposal we use a uniform prior for the regression parameters, random effects variance parameter, and the mixing proportion, and we use a partially proper non-informative prior distribution for the two unit-level error variance components in the mixture. We apply our method to two examples to predict summary characteristics of farm products at the small area level. One of the examples is prediction of twelve county-level crop areas cultivated for corn in some Iowa counties. The other example involves total cash associated in farm operations in twenty-seven farming regions in Australia. We compare predictions of small area characteristics based on the proposed method with those obtained by applying the Datta and Ghosh (Annals Stat. 19, 1748–1770, 1991) and the Chakraborty et al. (Int. Stat. Rev. 87, 158–176, 2019) HB methods. Our simulation study comparing these three Bayesian methods, when the unit-level error distribution is normal, or t, or two-component normal mixture, showed the superiority of our proposed method, measured by prediction mean squared error, coverage probabilities and lengths of credible intervals for the small area means.
Keywords: Nested error regression; Outliers; Prediction intervals and uncertainty; Robust empirical best linear unbiased prediction; Primary 62F15; Secondary 62D05 (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
http://link.springer.com/10.1007/s13571-019-00216-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:spr:sankhb:v:83:y:2021:i:1:d:10.1007_s13571-019-00216-8
Ordering information: This journal article can be ordered from
Access Statistics for this article
Sankhya B: The Indian Journal of Statistics is currently edited by Dipak Dey
More articles in Sankhya B: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().