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Entropy Measures for Stochastic Processes with Applications in Functional Anomaly Detection

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  • Hernández Banadik, Nicolás Jorge
  • Martos, Gabriel
  • Muñoz García, Alberto
  • Moguerza, Javier M.

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.

Suggested Citation

  • Hernández Banadik, Nicolás Jorge & Martos, Gabriel & Muñoz García, Alberto & Moguerza, Javier M., 2018. "Entropy Measures for Stochastic Processes with Applications in Functional Anomaly Detection," DES - Working Papers. Statistics and Econometrics. WS 26915, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:26915
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    Cited by:

    1. Gregova Elena, 2014. "Quality of business environment in Slovakia from the point of view of small enterprises," Annals of marketing-mba, Department of Marketing, Marketing MBA (RSconsult), vol. 2, August.
    2. Urazgaliev Vladimir S., 2014. "The main directions of small and medium business development in Russia," Annals of marketing-mba, Department of Marketing, Marketing MBA (RSconsult), vol. 2, August.

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    Keywords

    entropy;

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