On the asymptotic distribution of Matusita’s overlapping measure

In this paper, we study the asymptotic distribution of the plug-in kernel density estimator of the Matusita's overlapping measure. By utilizing the convergence of functional of stochastic processes, we show, under certain conditions, that the asymptotic distribution of the plug-in kernel density estimator (KDE) of Matusita's overlapping measure is normal distribution. Also, a small simulation study is conducted to support the theoretical finding of this paper. Furthermore, we apply our finding to a breast cancer data.