On the asymptotic distribution of Matusita's overlapping measure

Abstract

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.

Keywords:

• Asymptotic distribution
• kernel density estimation
• limiting distribution
• Matusita's overlapping measure
• breast cancer

AMS Subject Classification:

• 62G07
• 62F12

Acknowledgments

The authors are grateful for the comments received from editor and referees. All their suggestions have been constructive contribution to the manuscript.