Gamma Kernel Intensity Estimation in Temporal Point Processes

• Published in: Communications in statistics. Simulation and computation Vol. 40; no. 8; pp. 1146 - 1162
• Main Authors: Marcon, G., Adelfio, G., Chiodi, M.
• Format: Journal Article
• Language: English
• Published: Colchester Taylor & Francis Group 01-09-2011; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Bounded domain; Computer simulation; Distribution theory; Estimators; Exact sciences and technology; Gamma kernel estimator; Intensity function; Kernels; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Parametric inference; Probability; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Seismic engineering; Seismic phenomena; Skewed distributions; Statistics; Stochastic models; Stochastic processes; Temporal logic; Temporal point processes; 60G55; 62G07; Statistical distribution; Non parametric estimation; Kernel estimation; Statistical estimation; Kernel estimator; Gamma distribution; Statistical method; Estimating function; Bounded domain; Point estimation; Point process; Numerical simulation; Gamma kernel estimator; Temporal point processes; Intensity function
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2011.563158

In this article, we propose a nonparametric approach for estimating the intensity function of temporal point processes based on kernel estimators. In particular, we use asymmetric kernel estimators characterized by the gamma distribution, in order to describe features of observed point patterns adequately. Some characteristics of these estimators are analyzed and discussed both through simulated results and applications to real data from different seismic catalogs.