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Title: Inference on compound Cox processes by means of PCP Authors:  Nuria Ruiz-Fuentes - University of Jaen (Spain)
Paula Bouzas - University of Granada (Spain) [presenting]
Abstract: The compound Cox process is characterized by whether its intensity or its mean process, so inference on these stochastic processes is essential. Having observed several sample paths of the counting process, functional data analysis and principal components prediction are powerful techniques to estimate and finally to predict them. This inference also allows predicting most of the statistics (mean, mode, probability of a new occurrence, etc.). Additionally, a goodness-of-fit test can be derived to assess if a new observed sample path follows a given compound Cox process. Taking into account that Cox processes with or without random deletions, simultaneous occurrences or a time-space are particular cases of a compound Cox processes, the inference presented can be applied in a variety of real cases. Some examples will illustrate the results.