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

Vitaliy Oryshchenko ()

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 7, 1603-1628

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.

Date: 2020
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DOI: 10.1080/03610926.2018.1563182

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