Semiparametric estimation of conditional intensity functions for space-time processes

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Abstract

When dealing with data coming from a space time inhomogeneous process, there is oftenthe need of obtaining reliable estimates of the conditional intensity function. Accordingto the field of application, intensity function can be estimated through some assessedparametric model, where parameters are estimated by Maximum Likelihood method. Ifwe are only in an exploratory context or we would like to assess the adequacy of theparametric model, some kind of nonparametric estimation is required. Often, isotropic oranisotropic kernel estimates can be used, e.g. using the Silverman rule for the choice ofthe windows sizes h (Silverman, 1986). When the purpose of the study is the estimationof h, we could try to choose h in order to have good predictive properties of the estimatedintensity function. As it is known, a direct ML approach cannot be followed, since wewould obtain degenerate estimates (putting mass only on observed points), unless we usea penalizing function, depending on some smoothing constrain
Lingua originaleEnglish
PagineCD-CD
Numero di pagine2
Stato di pubblicazionePublished - 2008

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