Semiparametric Dynamic Proportional Intensity Models

Abstract

In this chapter, we discuss dynamic extensions of the proportional intensity (PI) model. This alternative class of models can be interpreted as the direct counterpart to the class of dynamic accelerated failure time (AFT) models considered in the previous chapter. As discussed in Chapter 2, a PI model can be estimated in different ways. One possibility is to adopt a fully parametric approach leading to a complete parameterization of the intensity, including also the baseline intensity function λ0(t). Such a model is consistently estimated by ML given that the chosen parameterization is correct. A further possibility is to refer to the results of Cox (1975) and to consistently estimate the parameter vector γ either by a partial likelihood approach or in a semiparametric way. In this framework, the model requires no specification of λ0(t) but of Λ0(ti−1, t i ) while λ0(t) is estimated semiparametrically or non-parametrically.1KeywordsPrice ChangeARMA ModelMonte Carlo StudyAutoregressive ParameterBaseline IntensityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.