Likelihood based inference for partially observed renewal processes

In this talk, we will be concerned with inference for renewal processes on the real line that are observed in a broken interval. For such processes, the classic history-based approach cannot be used. Instead, we adapt tools from sequential spatial point process theory to propose a Monte Carlo maximum likelihood estimator that takes into account the missing data. Its efficacy is assessed by means of a simulation study and the missing data reconstruction is illustrated on real data about calls to a medical helpline.