Functional Estimation of the Random Rate of a Cox Process

  • Paula R. Bouzas
  • Ana M. Aguilera
  • Nuria Ruiz-Fuentes


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.


Cox process Monotone piecewise cubic interpolation Functional principal component analysis Functional data analysis 

AMS 2000 Subject Classification

60G51 60G55 62H25 46N30 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Paula R. Bouzas
    • 1
  • Ana M. Aguilera
    • 1
  • Nuria Ruiz-Fuentes
    • 2
  1. 1.Department of Statistics and Operations ResearchUniv. GranadaGranadaSpain
  2. 2.Department of Statistics and Operations ResearchUniv. JaénJaénSpain

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