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Functional Estimation of the Random Rate of a Cox Process

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Abstract

The intensity of a doubly stochastic Poisson process (DSPP) is also a stochastic process whose integral is the mean process of the DSPP. From a set of sample paths of the Cox process we propose a numerical method, preserving the monotone character of the mean, to estimate the intensity on the basis of the functional PCA. A validation of the estimation method is presented by means of a simulation as well as a comparison with an alternative estimation method.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, Univ. Granada, 18071, Granada, Spain

    Paula R. Bouzas & Ana M. Aguilera

  2. Department of Statistics and Operations Research, Univ. Jaén, 23071, Jaén, Spain

    Nuria Ruiz-Fuentes

Authors
  1. Paula R. Bouzas
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  2. Ana M. Aguilera
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  3. Nuria Ruiz-Fuentes
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Corresponding author

Correspondence to Paula R. Bouzas.

Additional information

This work was partially supported by projects MTM2007-63793 of Dirección General de Investigación, Ministerio de Ciencia, P06-FQM-01470 from Consejería de Innovación, Ciencia y Empresa de la Junta de Andalucía and MTM2007-66791 of Plan Nacional I+D, Ministerio de Ciencia y Tecnología jointly by the FEDER and grant FQM-307 of Conserjería de Innovación de la Junta de Andalucía, all of them in Spain.

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Bouzas, P.R., Aguilera, A.M. & Ruiz-Fuentes, N. Functional Estimation of the Random Rate of a Cox Process. Methodol Comput Appl Probab 14, 57–69 (2012). https://doi.org/10.1007/s11009-010-9173-z

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  • DOI: https://doi.org/10.1007/s11009-010-9173-z

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