  Empirical best linear unbiased prediction (EBLUP) method uses a linear mixed
model in combining information from different sources of information. This
method is particularly useful in small area problems. The variability of an
EBLUP is traditionally measured by the mean squared prediction error (MSPE),
and interval estimates are generally constructed using estimates of the MSPE.
Such methods have shortcomings like under-coverage or over-coverage, excessive
length and lack of interpretability. We propose a parametric bootstrap approach
to estimate the entire distribution of a suitably centered and scaled EBLUP.
The bootstrap histogram is highly accurate, and differs from the true EBLUP
distribution by only $O(d^3n^{-3/2})$, where $d$ is the number of parameters
and $n$ the number of observations. This result is used to obtain highly
accurate prediction intervals. Simulation results demonstrate the superiority
of this method over existing techniques of constructing prediction intervals in
linear mixed models.
