The Bandwidth from the Density Power Divergence

Ro Jin Pak
2014 Communications for Statistical Applications and Methods  
The most widely used optimal bandwidth is known to minimize the mean integrated squared error(MISE) of a kernel density estimator from a true density. In this article proposes, we propose a bandwidth which asymptotically minimizes the mean integrated density power divergence(MIDPD) between a true density and a corresponding kernel density estimator. An approximated form of the mean integrated density power divergence is derived and a bandwidth is obtained as a product of minimization based on
more » ... mization based on the approximated form. The resulting bandwidth resembles the optimal bandwidth by Parzen (1962) , but it reflects the nature of a model density more than the existing optimal bandwidths. We have one more choice of an optimal bandwidth with a firm theoretical background; in addition, an empirical study we show that the bandwidth from the mean integrated density power divergence can produce a density estimator fitting a sample better than the bandwidth from the mean integrated squared error.
doi:10.5351/csam.2014.21.5.435 fatcat:6wezbuxipbdpjmzprpfnvgfcu4