Nonparametric Estimation of the Intensity Function of a Point Process
Tuesday, November 13, 2001 - 9:30am - 10:30am
Keh-Shin Lii (University of California)
Applications of point processes are numerous. They include the modeling of earthquakes in geophysics, stock market data in economic, crime occurrence in social science and traffic accidents among others. Most statistical properties of a point process can be determined by their intensity functions. Therefore, it is crucial to model and estimate intensity functions. There are many approaches proposed in the literature. A new approach to model intensity function processes is proposed for the class of the doubly stochastics Poisson processes. The intensity process is modeled by the sum of a homogeneous Poisson process with an unknown constant intensity component and a nonhomogeneous part with rate which is the convolution of a non-negative generating function g and a homogeneous Poisson point process with unit rate. A nonparametric estimator of the intensity function process is proposed and investigated. This research effort focuses on the use of second and higher-order Fourier transform techniques to estimate the generating function and the rate of the Poisson component. It is shown that the generating function can be estimated consistently. The estimated generating function can be used to generate the intensity function process. Predictions can then be obtained from intensity function process. Simulations and real data are used to demonstrate the method.