Statistical Inference with synthetic functional data derived from point processes with applications

W. González Manteiga, M. I. Borrajo García, I. Fuentes Santos

A common question when a given point process is observed in more than one population is whether those patterns share the same structure or they can be partitioned in a certain number of groups. The distribution of two point processes can be compared through recently developed nonparametric tests. However, classification of point processes into groups requires moving to the space of density functions, i.e. a synthetic data framework.

Clustering algorithms for functional data, such as the k-means, have been developed. However, the space of density functions is not Hilbert and, consequently the clustering algorithm needs to be conducted in a representation space. In this talk, we propose some procedures to generate this space, and we compare their performance in a simulation study.

The methodology presented is also applied to different real data problems: COVID-19 infections and deaths in Spain, wildfires in Galicia (north-west Spain) and crime events in Rio de Janeiro (Brazil).

Keywords: Functional data, Point process, clustering.

SGAPEIO-SEIO Invited Session
November 8, 2023  10:10 AM
CC2: Conference Room

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