  In this article, we construct empirical likelihood (EL)-weighted estimators
of linear functionals of a probability measure in the presence of side
information. Motivated by nuisance parameters in semiparametric models with
possibly infinite dimensions, we consider the use of estimated constraint
functions and allow the number of constraints to grow with the sample size. We
study the asymptotic properties and efficiency gains. The results are used to
construct improved estimators of parameters in structural equation models. The
EL-weighted estimators of parameters are shown to have reduced variances in a
SEM in the presence of side information of stochastic independence of the
random error and random covariate. Some simulation results on efficiency gain
are reported.
