THE EXPONENTIAL KERNEL IN DENSITY ESTIMATION

A. R. Mugdadi (U. S. A.) and A. M. Lahrech (U. S. A.)

Abstract

The assumption of symmetry of kernel functions in kernel density estimation simplifies many complicated formulas. In this investigation we dropped this assumption by using the exponential kernel to evaluate the asymptotic mean integrated square error and the optimal bandwidth. Also, we used the exponential kernel in three well known data based methods to select the bandwidth. In addition we compare between the exponential and the Gaussian kernels based on simulations and a real life data.

Keywords and phrases: kernel estimators, bandwidth selection, mean square error, least square cross validation, biased cross validation, plug-in.