  In this paper, we propose new semiparametric procedures for making inference
on linear functionals and their functions of two semicontinuous populations.
The distribution of each population is usually characterized by a mixture of a
discrete point mass at zero and a continuous skewed positive component, and
hence such distribution is semicontinuous in the nature. To utilize the
information from both populations, we model the positive components of the two
mixture distributions via a semiparametric density ratio model. Under this
model setup, we construct the maximum empirical likelihood estimators of the
linear functionals and their functions, and establish the asymptotic normality
of the proposed estimators. We show the proposed estimators of the linear
functionals are more efficient than the fully nonparametric ones. The developed
asymptotic results enable us to construct confidence regions and perform
hypothesis tests for the linear functionals and their functions. We further
apply these results to several important summary quantities such as the
moments, the mean ratio, the coefficient of variation, and the generalized
entropy class of inequality measures. Simulation studies demonstrate the
advantages of our proposed semiparametric method over some existing methods.
Two real data examples are provided for illustration.
