The Annals of Statistics

Smoothing Counting Process Intensities by Means of Kernel Functions

Henrik Ramlau-Hansen

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Abstract

The kernel function method developed during the last twenty-five years to estimate a probability density function essentially is a way of smoothing the empirical distribution function. This paper shows how one can generalize this method to estimate counting process intensities using kernel functions to smooth the nonparametric Nelson estimator for the cumulative intensity. The properties of the estimator for the intensity itself are investigated, and uniform consistency and asymptotic normality are proved. We also give an illustrative numerical example.

Article information

Source
Ann. Statist. Volume 11, Number 2 (1983), 453-466.

Dates
First available: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176346152

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176346152

Mathematical Reviews number (MathSciNet)
MR696058

Zentralblatt MATH identifier
0514.62050

Subjects
Primary: 60G55: Point processes
Secondary: 62G05: Estimation 62P05: Applications to actuarial sciences and financial mathematics

Keywords
Smoothing counting processes kernel functions intensities

Citation

Ramlau-Hansen, Henrik. Smoothing Counting Process Intensities by Means of Kernel Functions. The Annals of Statistics 11 (1983), no. 2, 453--466. doi:10.1214/aos/1176346152. http://projecteuclid.org/euclid.aos/1176346152.


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