Bootstrap MISE Estimators to Obtain Bandwidth for Kernel Density Estimation

Abstract

Research in the area of bandwidth selection was an active topic in the 1980s and 1990s, however, recently there has been little research in the area. We re-opened this investigation and have found a new method for estimating mean integrated squared error for kernel density estimators. We provide an overview of other methods to obtain optimal bandwidths and offer a comparison of these methods via a simulation study. In certain situations, our method of estimating an optimal bandwidth yields a smaller MISE than competing methods to compute bandwidths. This procedure is illustrated by an application to two data sets.

Keywords:

• Bandwidth
• Bootstrap
• Kernel density
• MSE

Mathematics Subject Classification:

• 62G07
• 62G30