Modelling the mean of a doubly stochastic Poisson process by functional data analysis

Computational Statistics and Data Analysis

Volumn 50, Issue 10, 2006, Pages 2655-2667

  Bouzas, P R ^a   Valderrama, M J ^a   Aguilera, A M ^a   Ruiz Fuentes, N ^b  

^a UNIVERSITY OF GRANADA   (Spain)

^b UNIVERSITY OF JAÉN   (Spain)

Author keywords

Doubly stochastic Poisson process; Functional data analysis; Functional principal component analysis; Monotone piecewise cubic interpolation

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER SIMULATION; DATA REDUCTION; ESTIMATION; INTERPOLATION; PRINCIPAL COMPONENT ANALYSIS; STOCHASTIC CONTROL SYSTEMS;

DOUBLY STOCHASTIC POISSON PROCESS; FUNCTIONAL DATA ANALYSIS; FUNCTIONAL PRINCIPAL COMPONENT ANALYSIS; MONOTONE PIECEWISE CUBIC INTERPOLATION;

POISSON DISTRIBUTION;

EID: 33646078793     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2005.04.015     Document Type: Article

References (19)

1. Aguilera A.M., Gutiérrez R., Ocaña F.A., and Valderrama M.J. Computational approaches to estimation in the principal component analysis of a stochastic process. Appl. Stochastic Models Data Anal. 11 4 (1995) 279-299
2. Aguilera A.M., Gutiérrez R., and Valderrama M.J. Approximation of estimators in the PCA of a stochastic process using B-splines. Comm. Statist. (Simulation) 25 3 (1996) 671-690
3. Benning, V.E., Korolev, V.Y., 2002. Generalized Poisson Models and Their Applications in Insurance and Finance. VSP, Utrecht.
4. Boel R., and Beneš V. Recursive nonlinear estimation of a diffusion acting as the rate of an observed Poisson process. IEEE Trans. Inform. Theory 26 5 (1980) 561-575
5. Bouzas P.R., Aguilera A.M., and Valderrama M.J. Forecasting a class of doubly stochastic Poisson processes. Statist. Papers 43 (2002) 507-523
6. Bouzas, P.R., Aguilera, A.M., Valderrama, M.J., Ruiz-Fuentes, N., 2004. On the structure of the stochastic process of mortgages in Spain. Comput. Statist., in press.
7. Brèmaud P. Point Processes and Queues: Martingale Dynamics (1981), Springer, New York
8. Daley D.J., and Vere-Jones D. An Introduction to the Theory of Point Processes (1988), Springer, New York
9. Escabias M., Aguilera A.M., and Valderrama M.J. Principal component estimation of functional logistic regression: discussion of two different approaches. J. Nonparametric Statist. 16 3-4 (2004) 365-384
10. Escabias M., Aguilera A.M., and Valderrama M.J. Modelling environmental data by functional principal component logistic regression. Envirometrics 16 1 (2004) 95-107
11. Fritsch F.N., and Carlson R.E. Monotone piecewise cubic interpolation. SIAM J. Numer. Anal. 17 2 (1980) 238-246
12. Grigoriu M. Applied Non-Gaussian Processes, Examples Theory, Simulation, Linear Random Vibration and MATLAB Solutions (1995), PTR Prentice-Hall, Englewood Cliffs, NJ
13. Last G., and Brandt A. Marked Point Processes on the Real Line. (The Dynamic Approach) (1995), Springer, New York
14. Ocaña, F.A., 1996. Alternativas geométricas en el ACP de una variable aleatoria Hilbertiana. Tesis Doctoral de la Universidad de Granada.
15. Ocaña, F.A., Aguilera, A.M., Valenzuela, O., 1998. A wavelet approach to functional principal component analysis. In: R. Payne, P. Green (Eds.), Proceedings of COMPSTAT 98. Physica-Verlag, Wurzburg, pp. 413-418.
16. Ramsay J.O., and Silverman B.M. Functional Data Analysis (1997), Springer, New Jersey
17. Rolski T., Schmidli H., Schmidt V., and Teugels J. Stochastic Processes for Insurance and Finance (2001), Wiley, Chichester, UK
18. Snyder D.L., and Miller M.I. Random Point Processes in Time and Space. second Ed (1991), Springer, New York
19. Valderrama, J.M., Aguilera, A.M., Ocaña, F.A., 2000. Predicción dinámica mediante análisis de datos funcionales. La Muralla, Madrid.