Paper Info
Title
Constrained empirical Bayes estimator and its uncertainty in normal linear mixed models
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.
Year
DOI
Venue
2013
10.1016/j.jmva.2013.08.012
J. Multivariate Analysis
Keywords
Field
DocType
empirical bayes estimator,larger estimation error,mse estimator,best linear unbiased predictor,asymptotic unbiased estimator,larger geographical area,asymptotic approximation,small area estimation,normal linear mixed model,aggregated mean,corresponding direct estimate,small area,benchmarking,linear mixed model,mean squared error,second order approximation
Econometrics,Best linear unbiased prediction,Mean squared error,Mixed model,Generalized linear mixed model,Statistics,Bayes estimator,Small area estimation,Mathematics,Bayes' theorem,Estimator
Journal
Volume
ISSN
Citations 
122,
0047-259X
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Tatsuya Kubokawa13611.73