Prediction of recurrent events
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In this thesis, we will study issues related to prediction problems and put an emphasis on those arising when recurrent events are involved. First we define the basic concepts of frequentist and Bayesian statistical prediction in the first chapter. In the second chapter, we study frequentist prediction intervals and their associated predictive distributions. We will then present an approach based on asymptotically uniform pivotals that is shown to dominate the plug-in approach under certain conditions. The following three chapters consider the prediction of recurrent events. The third chapter presents different prediction models when these events can be modeled using homogeneous Poisson processes. Amongst these models, those using random effects are shown to possess interesting features. In the fourth chapter, the time homogeneity assumption is relaxed and we present prediction models for non-homogeneous Poisson processes. The behavior of these models is then studied for prediction problems with a finite horizon. In the fifth chapter, we apply the concepts discussed previously to a warranty dataset coming from the automobile industry. The number of processes in this dataset being very large, we focus on methods providing computationally rapid prediction intervals. Finally, we discuss the possibilities of future research in the last chapter.