MISE of a kernel density estimator

Santanu Dutta

Abstract

Mean Integrated Squared Error (MISE) of a kernel density estimator is a popular measure of accuracy of a kernel density estimator. It provides insight to many important aspects (e.g. rate of convergence, choice of bandwidth and kernel order ) of a density estimator. We review some of the important existing results in this context. In general MISE is unknown, so the problem of estimating MISE is addressed. We review some of the existing methods and present some new results in the context of estimating MISE by bootstrap method. The problem of data based bandwidth selection is also addressed.