The linear mixed models (LMM) and the empirical best linear unbiased predictor
(EBLUP) induced from LMM have been well studied and extensively used for a long
time in many applications. Of these, EBLUP in small area estimation has been
recognized as a useful tool in various practical statistics. In this paper, we give a
review on LMM and EBLUP from a aspect of small area estimation. Especially, we
explain why EBLUP is likely to be reliable. The reason is that EBLUP possesses
the shrinkage function and the pooling effects as desirable properties, which arise
from the setup of random effects and common paramers in LMM. Such important
properties of EBLUP are clarified as well as some recent results of the mean squared
error estimation, the confidence interval and the variable selection procedures are
summarized.
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