  Small area estimation under linear mixed models often assumes that the small
area effect is random effect in almost all previous studies. However, in this
paper a new approach is proposed explaining small area effect as the unknown
function of an area-indicative variable, which is a kind of semiparametric
models. The nonparametric part for area effect is represented by using
penalized splines, from which the estimation and inference are done in the
linear mixed model framework. The mean-squared error of empirical estimators is
shown, and the testing for small area effect also considered. Additionally,
some numerical simulations are demonstrated to express the good performance of
this method.
