The choice of a kernel function in the graduation of counting process intensities

1 July 1983

journal article
research article
Published by Taylor & Francis in Scandinavian Actuarial Journal

Vol. 1983 (3) , 165-182
https://doi.org/10.1080/03461238.1983.10408700

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 & Müller 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.

Keywords

This publication has 8 references indexed in Scilit:

On the theory of moving average graduation
Scandinavian Actuarial Journal, 1979
Kernel estimation of regression functions
Published by Springer Nature ,1979
Optimal convergence properties of kernel estimates of derivatives of a density function
Published by Springer Nature ,1979
Nonparametric Inference for a Family of Counting Processes
The Annals of Statistics, 1978
Curve Estimates
The Annals of Mathematical Statistics, 1971
Non-Parametric Estimation of a Multivariate Probability Density
Theory of Probability and Its Applications, 1969
On Estimation of a Probability Density Function and Mode
The Annals of Mathematical Statistics, 1962
Remarks on Some Nonparametric Estimates of a Density Function
The Annals of Mathematical Statistics, 1956