JSM 2004 - Toronto

Abstract #302215

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Activity Number: 268
Type: Topic Contributed
Date/Time: Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #302215
Title: Local Likelihood Intensity Estimation
Author(s): Jennifer L. Prokop*+
Companies: University of Western Ontario
Address: Department of Statistics & Actuarial Science, London, ON, N6A 5B7, Canada
Keywords: point processes ; smoothing
Abstract:

In a series of papers, Brillinger has demonstrated the usefulness of nonparametric intensity function estimation in the study of temporal point process data. An alternative approach is local likelihood estimation using a flexible conditional intensity model. Local polynomial approximations are used for the logarithm of the conditional intensity and, as in Hjort and Jones (1996), we define a local kernel-smoothed log likelihood function. Parameter estimation is done via maximizing the localized version of the log likelihood. We show that, for the class of self-exciting processes, the local constant cross-intensity function estimator is not equivalent to Brillinger's cross-intensity estimator. Simulation is employed to compare the quality of the intensity function estimators.

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