Exact mean integrated squared error and bandwidth selection for kernel distribution function estimators

Abstract

An exact, closed form, and easy to compute expression for the mean integrated squared error (MISE) of a kernel estimator of a normal mixture cumulative distribution function is derived for the class of arbitrary order Gaussian-based kernels. Comparisons are made with MISE of the empirical distribution function, the infeasible minimum MISE, and the uniform kernel. A simple plug-in method of simultaneously selecting the optimal bandwidth and kernel order is proposed based on a non asymptotic approximation of the unknown distribution by a normal mixture. A simulation study shows that the method provides a viable alternative to existing bandwidth selection procedures.

Keywords:

• Finite sample
• Gaussian-based kernel
• uniform kernel
• normal mixture
• plug-in rule
• smoothing

MSC 2010 subject classifications:

• 62G05

Disclosure statement

No potential conflict of interest was reported by the author.