TY - CONF

T1 - Semi-parametric estimation of conditional intensity functions in inhomogeneous space-time point processes

AU - Adelfio, Giada

AU - Chiodi, Marcello

AU - Luzio, Dario

PY - 2009

Y1 - 2009

N2 - Dealing with data coming from a space-time inhomogeneous process, there is often theneed of obtaining estimates of the conditional intensity function, without a complete defi nition of a parametric model and so nonparametric estimation is required: isotropic or anisotropic kernel estimates can be used. The properties of the intensities estimated are not always good, expecially in seismological field. We could try to choose the bandwidth in order to have good predictive properties of the estimated intensity function. Since a direct ML approach can not be followed, we use an estimation procedure based on the further increments of likelihood obtained adding a new observation. Similarly to cross validation criterion, we consider additive contributions given bythe log-likelihood of the (m+ 1)th observed point given the nonparametric estimationbased on the fi rst m observations.

AB - Dealing with data coming from a space-time inhomogeneous process, there is often theneed of obtaining estimates of the conditional intensity function, without a complete defi nition of a parametric model and so nonparametric estimation is required: isotropic or anisotropic kernel estimates can be used. The properties of the intensities estimated are not always good, expecially in seismological field. We could try to choose the bandwidth in order to have good predictive properties of the estimated intensity function. Since a direct ML approach can not be followed, we use an estimation procedure based on the further increments of likelihood obtained adding a new observation. Similarly to cross validation criterion, we consider additive contributions given bythe log-likelihood of the (m+ 1)th observed point given the nonparametric estimationbased on the fi rst m observations.

KW - conditional intensity function

KW - forward likelihood predictive estimation

KW - kernel estimator

KW - conditional intensity function

KW - forward likelihood predictive estimation

KW - kernel estimator

UR - http://hdl.handle.net/10447/40440

M3 - Other

ER -