### Abstract

The following steps are suggested for smoothing the occurrence patternsin a clustered space–time process, in particular the data from an earthquake catalogue.First, the original data is fitted by a temporal version of the ETAS model, and the occurrencetimes are transformed by using the cumulative form of the fitted ETAS model.Then the transformed data (transformed times and original locations) is smoothedby a space–time kernel with bandwidth obtained by optimizing a naive likelihoodcross-validation. Finally, the estimated intensity for the original data is obtained byback-transforming the estimated intensity for the transformed data. This techniqueis used to estimate the intensity for earthquake occurrence data for associated withcomplex sequences of events off the East Coast of Tohoku district, northern Japan.The intensity so obtained is compared to the conditional intensity estimated from afull space–time ETAS model for the same data.

Lingua originale | English |
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Numero di pagine | 18 |

Rivista | Annals of the Institute of Statistical Mathematics |

Volume | 62 |

Stato di pubblicazione | Published - 2010 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability