Entropy Measures for Stochastic Processes with Applications in Functional Anomaly Detection

Gabriel Martos, Nicolás Hernández, Alberto Muñoz, Javier M. Moguerza

Abstract: We propose a definition of entropy for stochastic processes. We provide a reproducing kernel Hilbert space model to estimate entropy from a random sample of realizations of a stochastic process, namely functional data, and introduce two approaches to estimate minimum entropy sets. These sets are relevant to detect anomalous or outlier functional data. A numerical experiment illustrates the performance of the proposed method; in addition, we conduct an analysis of mortality rate curves as an interesting application in a real-data context to explore functional anomaly detection.