Consistent parametric estimation of the intensity of a spatial–temporal point process |
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| Institution: | 1. University of Georgia, College of Public Health, Department of Epidemiology and Biostatistics, Athens, Georgia, United States;2. Zhejiang Provincial Center for Disease Control and Prevention, Hangzhou, China;3. University of Georgia, College of Public Health, Health Informatics Institute, Athens, Georgia, United States;4. University of Georgia, Center for the Ecology of Infectious Diseases, Athens, Georgia, United States;5. Boston University, School of Public Health, Department of Epidemiology, Boston, Massachusetts, United States;6. University of Georgia, Department of Statistics, Athens, Georgia, United States;7. Tulane University, School of Public Health and Tropical Medicine, Department of Epidemiology, New Orleans, Louisiana, United States;8. Renmin University of China, Center for Applied Statistics, Beijing, China;9. Renmin University of China, School of Statistics, Beijing, China;10. Renmin University of China, Statistical Consulting Center, Beijing, China |
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| Abstract: | We consider conditions under which parametric estimates of the intensity of a spatial–temporal point process are consistent. Although the actual point process being estimated may not be Poisson, an estimate involving maximizing a function that corresponds exactly to the log-likelihood if the process is Poisson is consistent under certain simple conditions. A second estimate based on weighted least squares is also shown to be consistent under quite similar assumptions. The conditions for consistency are simple and easily verified, and examples are provided to illustrate the extent to which consistent estimation may be achieved. An important special case is when the point processes being estimated are in fact Poisson, though other important examples are explored as well. |
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