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Mixed Effects Prediction under Benchmarking and Applications to Small Area Estimation
en
Benchmarking
best linear unbiased predictor
constrained Bayes
empirical Bayes
linear mixed model
mean squared error
parametric bootstrap
second-order approximation
small area estimation
Kubokawa Tatsuya
The 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 EBLUP 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 EBLUP 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 the constrained EBLUP may have a larger estimation error than EBLUP. In this paper, we address this issue by deriving asymptotic approximations of MSE of the constrained EBLUP. Also, we provide asymptotic unbiased estimators of the MSE of the constrained EBLUP based on the parametric bootstrap method, and establish their second-order justification. Finally, the performances of the suggested MSE estimators are numerically investigated.
本文フィルはリンク先を参照のこと
Discussion paper series. CIRJE-F
CIRJE-F-832
2012-01
AA11450569
application/pdf
335
日本経済国際共同センター
http://www.cirje.e.u-tokyo.ac.jp/research/dp/2012/2012cf832ab.html