Abstract
Abstract Since Rosenblatt introduced the kernel function estimator for a probability density, several authors have studied the properties of the kernel estimator and the choice of the kernel function. In a companion paper, the author has shown how it is possible to use kernel functions to estimate counting process intensities instead of only their integrated counterparts. In the present paper, we discuss in detail how the kernel function may be chosen. We show that the kernel functions obtained previously by Epanechnikov and Gasser & Muller may be derived in a manner quite different from theirs, and that they and Bartlett's kernel have properties one has not been aware of before. Furthermore, the close relationship between graduation by kernel functions an by moving averages is demonstrated and is used to infer new results about the latter.
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