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. Espe-
cially, we explain why EBLUP is likely to be reliable. The reason is that EBLUP
possesses the shrinkage function and the pooling e ects as desirable properties,
which arise from the setup of random e ects and common parameters in LMM.
Such important properties of EBLUP are clari ed as well as some recent results
of the mean squared error estimation, the con dence interval and the variable
selection procedures are summarized.