Smoothing Counting Process Intensities by Means of Kernel Functions
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.
Permanent link to this document: http://projecteuclid.org/euclid.aos/1176346152
Digital Object Identifier: doi:10.1214/aos/1176346152
Mathematical Reviews number (MathSciNet): MR696058
Zentralblatt MATH identifier: 0514.62050