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Forward likelihood‐based predictive approach for space–time point processes
Author(s) -
Chiodi Marcello,
Adelfio Giada
Publication year - 2011
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.1121
Subject(s) - estimator , point process , computer science , parametric statistics , kernel density estimation , nonparametric statistics , likelihood function , estimation , point estimation , function (biology) , point (geometry) , kernel (algebra) , statistics , econometrics , mathematics , estimation theory , algorithm , geometry , management , evolutionary biology , economics , biology , combinatorics
Dealing with data from a space–time point process, the estimation of the conditional intensity function is a crucial issue even if a complete definition of a parametric model is not available. In particular, in case of exploratory contexts or if we want to assess the adequacy of a specific parametric model, some kind of nonparametric estimation procedure could be useful. Often, for these purposes kernel estimators are used and the estimation of the intensity function depends on the estimation of bandwidth parameters. In some fields, like for instance the seismological one, predictive properties of the estimated intensity function are pursued. Since a direct ML approach cannot be used, we propose an estimation procedure based on the subsequent increments of likelihood obtained adding an observation one at a time. Simulated results and some applications to statistical seismology are provided. Copyright © 2011 John Wiley & Sons, Ltd.