TY - JOUR

T1 - Hybrid kernel estimates of space-time earthquake occurrence rates using the Etas model

AU - Adelfio, Giada

AU - Ogata, Yosihiko

PY - 2010

Y1 - 2010

N2 - The following steps are suggested for smoothing the occurrence patterns
in 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 occurrence
times are transformed by using the cumulative form of the fitted ETAS model.
Then the transformed data (transformed times and original locations) is smoothed
by a space–time kernel with bandwidth obtained by optimizing a naive likelihood
cross-validation. Finally, the estimated intensity for the original data is obtained by
back-transforming the estimated intensity for the transformed data. This technique
is used to estimate the intensity for earthquake occurrence data for associated with
complex sequences of events off the East Coast of Tohoku district, northern Japan.
The intensity so obtained is compared to the conditional intensity estimated from a
full space–time ETAS model for the same data.

AB - The following steps are suggested for smoothing the occurrence patterns
in 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 occurrence
times are transformed by using the cumulative form of the fitted ETAS model.
Then the transformed data (transformed times and original locations) is smoothed
by a space–time kernel with bandwidth obtained by optimizing a naive likelihood
cross-validation. Finally, the estimated intensity for the original data is obtained by
back-transforming the estimated intensity for the transformed data. This technique
is used to estimate the intensity for earthquake occurrence data for associated with
complex sequences of events off the East Coast of Tohoku district, northern Japan.
The intensity so obtained is compared to the conditional intensity estimated from a
full space–time ETAS model for the same data.

KW - Bandwidths · Shape parameters · Cross-validation · ETAS models · Intensity function · Kernel estimates · Space–time point processes · Space–time ETAS model · Transformation of time

UR - http://hdl.handle.net/10447/52921

UR - http://hdl.handle.net/10.1007/s10463-009-0268-7

M3 - Article

VL - 62

SP - -

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

ER -