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Statistical inference for doubly stochastic multichannel Poisson processes: A PCA approach

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  • Fernández-Alcalá, R.M.
  • Navarro-Moreno, J.
  • Ruiz-Molina, J.C.

Abstract

Efficient computational algorithms for making inferences about the intensity process of an observed doubly stochastic multichannel Poisson process are designed. The proposed solution is based on a numerical version of principal component analysis (PCA) of stochastic processes and hence it can be applied simply with knowledge of the first- and second-order moments of the intensity process of interest. The technique provided is valid for solving all types of estimation problems: filtering, prediction and smoothing.

Suggested Citation

  • Fernández-Alcalá, R.M. & Navarro-Moreno, J. & Ruiz-Molina, J.C., 2009. "Statistical inference for doubly stochastic multichannel Poisson processes: A PCA approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4322-4331, October.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4322-4331
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    References listed on IDEAS

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    1. Bouzas, P.R. & Valderrama, M.J. & Aguilera, A.M. & Ruiz-Fuentes, N., 2006. "Modelling the mean of a doubly stochastic Poisson process by functional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2655-2667, June.
    2. Preda, C. & Saporta, G., 2005. "Clusterwise PLS regression on a stochastic process," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 99-108, April.
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    4. Preda, C. & Saporta, G., 2005. "PLS regression on a stochastic process," Computational Statistics & Data Analysis, Elsevier, vol. 48(1), pages 149-158, January.
    5. Aguilera, Ana M. & Escabias, Manuel & Valderrama, Mariano J., 2006. "Using principal components for estimating logistic regression with high-dimensional multicollinear data," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 1905-1924, April.
    6. LeSage, James & Banerjee, Sudipto & Fischer, Manfred M. & Congdon, Peter, 2009. "Spatial statistics: Methods, models & computation," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2781-2785, June.
    7. Centanni, Silvia & Minozzo, Marco, 2006. "A Monte Carlo Approach to Filtering for a Class of Marked Doubly Stochastic Poisson Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1582-1597, December.
    8. Hossain, Md. Monir & Lawson, Andrew B., 2009. "Approximate methods in Bayesian point process spatial models," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2831-2842, June.
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