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Functional Estimation of the Random Rate of a Cox Process

Author

Listed:
  • Paula R. Bouzas

    (Univ. Granada)

  • Ana M. Aguilera

    (Univ. Granada)

  • Nuria Ruiz-Fuentes

    (Univ. Jaén)

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.

Suggested Citation

  • Paula R. Bouzas & Ana M. Aguilera & Nuria Ruiz-Fuentes, 2012. "Functional Estimation of the Random Rate of a Cox Process," Methodology and Computing in Applied Probability, Springer, vol. 14(1), pages 57-69, March.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:1:d:10.1007_s11009-010-9173-z
    DOI: 10.1007/s11009-010-9173-z
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    References listed on IDEAS

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    1. N. Locantore & J. Marron & D. Simpson & N. Tripoli & J. Zhang & K. Cohen & Graciela Boente & Ricardo Fraiman & Babette Brumback & Christophe Croux & Jianqing Fan & Alois Kneip & John Marden & Daniel P, 1999. "Robust principal component analysis for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 1-73, June.
    2. Ana M. Aguilera & Ramón Gutiérrez & Francisco A. Ocaña & Mariano J. Valderrama, 1995. "Computational approaches to estimation in the principal component analysis of a stochastic process," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 11(4), pages 279-299, December.
    3. Ocaña, F. A. & Aguilera, A. M. & Valderrama, M. J., 1999. "Functional Principal Components Analysis by Choice of Norm," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 262-276, November.
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    Cited by:

    1. Paula R. Bouzas & Nuria Ruiz-Fuentes & Carmen Montes-Gijón & Juan Eloy Ruiz-Castro, 2021. "Forecasting counting and time statistics of compound Cox processes: a focus on intensity phase type process, deletions and simultaneous events," Statistical Papers, Springer, vol. 62(1), pages 235-265, February.

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