  This article studies the asymptotic behaviors of nonparametric estimators of
two overlapping measures, namely Pianka's and MacArthur-Levins measures. The
plug-in principle and the method of kernel density estimation are used to
estimate such measures. The limiting theory of the functional of stochastic
processes is used to study limiting behaviors of these estimators. It is shown
that both limiting distributions are normal under suitable assumptions. The
results are obtained in more general conditions on density functions and their
kernel estimators. These conditions are suitable to deal with various
applications. A small simulation study is also conducted to support the
theoretical findings. Finally, a real data set has been analyzed for
illustrative purposes.
