Multivariate Global-Local Priors for Small Area Estimation

Tamal Ghosh, Malay Ghosh, Jerry J. Maples and Xueying Tang
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Tamal Ghosh: Citibank, Tampa, FL 33610, USA
Malay Ghosh: Department of Statistics, University of Florida, Gainesville, FL 32611, USA
Jerry J. Maples: United States Bureau of the Census, Washington, DC 20233, USA
Xueying Tang: Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA

Stats, 2022, vol. 5, issue 3, 1-16

Abstract: It is now widely recognized that small area estimation (SAE) needs to be model-based. Global-local (GL) shrinkage priors for random effects are important in sparse situations where many areas’ level effects do not have a significant impact on the response beyond what is offered by covariates. We propose in this paper a hierarchical multivariate model with GL priors. We prove the propriety of the posterior density when the regression coefficient matrix has an improper uniform prior. Some concentration inequalities are derived for the tail probabilities of the shrinkage estimators. The proposed method is illustrated via both data analysis and simulations.

Keywords: global-local prior; small area estimation; shrinkage estimators; concentration inequalities; hierarchical multivariate model; posterior density (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jstats:v:5:y:2022:i:3:p:40-688:d:871104

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