Constrained empirical Bayes estimator and its uncertainty in normal linear mixed models

Tatsuya Kubokawa

Journal of Multivariate Analysis, 2013, vol. 122, issue C, 377-392

Abstract: The empirical Bayes (EB) estimator or empirical best linear unbiased predictor (EBLUP) in the linear mixed model (LMM) is useful for the small area estimation in the sense of increasing the precision of estimation of small area means. However, one potential difficulty of EB is that when aggregated, the overall estimate for a larger geographical area may be quite different from the corresponding direct estimate like the overall sample mean. One way to solve this problem is the benchmarking approach, and the constrained EB (CEB) is a feasible solution which satisfies the constraints that the aggregated mean and variance are identical to the requested values of mean and variance. An interesting query is whether CEB may have a larger estimation error than EB. In this paper, we address this issue by deriving asymptotic approximations of MSE of CEB. Also, we provide asymptotic unbiased estimators for MSE of CEB based on the parametric bootstrap method, and establish their second-order justification. Finally, the performance of the suggested MSE estimators is numerically investigated.

Keywords: Benchmarking; Best linear unbiased predictor; Constrained Bayes; Empirical Bayes; Linear mixed model; Mean squared error; Parametric bootstrap; Second-order approximation; Small area estimation (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X13001735
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:122:y:2013:i:c:p:377-392

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2013.08.012

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().