Abstract
An estimator for the intensity process of a doubly stochastic Poisson process is presented, having no statistical previous knowledge of it. In order to give a statistical structure of the intensity, a functional Principal Components Analysis is applied to k estimated sample paths of the intensity built from k observed sample paths of the point process.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Boel, R. and Benes, V. (1980). Recursive Nonlinear Estimation of a Diffusion Acting as the Rate of an Observed Poisson Process. IEEE Transactions on Information Theory, 26 (5), 561–575.
Bouzas, P.R., Aguilera, A.M. and Valderrama, M.J. (2002). Forecasting a class of Doubly Stochastic Poisson Process. Statistical Papers, in press.
Di Paola, M. and Falsone, G (1999). Higher order statistics of the response of linear systems excited by polynomials of filtered Poisson pulses. Probabilistic Engineering Mechanics, 14, 55–62.
Grigoriu, M. (1995). Applied non-gaussian processes. Prentice Hall: New Jersey.
Grigoriu, M. (2000). A spectral representation based model for Monte Carlo Simulation. Probabilistic Engineering Mechanics, 15, 365–370.
Landers, T.L., Jiang, S.T. and Peek, J.R. (2001). Semi-parametric PWP model robustness for log-linear increasing rates of occurrence of failures. Reliability Engineering and System Safety, 73, 145–153.
Last, G. and Brandt, A. (1995). Marked Point processes on the real line. (The dynamic approach). Springer-Verlag: New York.
Ochi, M.K. (1990). Applied Probability and Stochastic Processes (In Engineering and Physical Sciences). Wiley: New York.
Ramsay, J.O. and Silverman, B.M. (1997). Functional data analysis. Springer-Verlag: New York.
Snyder, D.L. and Miller, M.I. (1991). Random point processes in time and space. (2nd Edition). Springer-Verlag: New York.
Valderrama, M.J., Aguilera, A.M. and Ocaña, F.A. (2000). Predicción dinámica mediante análisis de datos funcionales. La Muralla-Hespérides: Madrid.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aguilera, A.M., Bouzas, P.R., Ruiz-Fuentes, N. (2002). Functional Principal Component Modelling of the Intensity of a Doubly Stochastic Poisson Process. In: Härdle, W., Rönz, B. (eds) Compstat. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57489-4_55
Download citation
DOI: https://doi.org/10.1007/978-3-642-57489-4_55
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-1517-7
Online ISBN: 978-3-642-57489-4
eBook Packages: Springer Book Archive