Rescaling marked point processes

Australian and New Zealand Journal of Statistics

Volumn 46, Issue 1, 2004, Pages 133-143

  Vere Jones, David ^a   Schoenberg, Frederic Paik ^b  

^a VICTORIA UNIVERSITY OF WELLINGTON   (New Zealand)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Compensator; Intensity; Meyer's theorem; Model evaluation; Poisson process; Random time change; Residual analysis

Indexed keywords

EID: 1842715073     PISSN: 13691473     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-842X.2004.00319.x     Document Type: Article

References (26)

1. AALEN, O. & HOEM, J. (1978). Random time changes for multivariate counting processes. Scand. Actuar. J., 81-101.
2. ANDERSEN, P.K., BORGAN, O., GILL, R.D & KEIDING, N. (1993). Statistical Models Based on Counting Processes. New York: Springer-Verlag.
3. BRÉMAUD, P.M. (1972). A martingale approach to point processes. Memorandum ERL-M345, Electronics Research Laboratory, University of California Berkeley, Berkeley, CA.
4. BROWN, T. & NAIR, M. (1988). A simple proof of the multivariate random time change theorem for point processes. J. Appl. Probab. 25, 210-214.
5. DALEY, D. & VERE-JONES, D. (1988). An Introduction to the Theory of Point Processes. New York: Springer.
6. DALEY, D. & VERE-JONES, D. (2003). An Introduction to me the Theory of Point Processes, 2nd edn, Vol. 1. New York & Berlin: Springer.
7. HJORT, N.L. (1990). Goodness of fit tests in models for life history data based on cumulative hazard rates. Ann. Statist. 18, 1221-1258.
8. JACOD, J. (1975). Multivariate point processes: predictable projections, Radon-Nikodym derivatives, representation of martingales. Z. Wahrsch. Verw. Gebiete 31, 235-253.
9. KALLENBERG, O. (1990). Random time change and an integral representation for marked stopping times. Probab. Theory Related Fields 86, 167-202.
10. KARR, A.F. (1986). Point Processes and their Statistical Inference. New York: Dekker.
11. KHMALADZE, E.V. (1981). Martingale approach to the goodness of fit tests. Theory Probab. Appl. 26, 246-265.
12. m. Ann. Statist. 16, 1503-1516.
13. KHMALADZE, E.V. (1993). Goodness of fit problem and scanning innovation martingales. Ann. Statist. 21, 798-829.
14. KNIGHT, F.B. (1970). An infinitesimal decomposition for a class of Markov processes. Ann. Math. Statist. 41, 1510-1529.
15. KURTZ, T.G. (1980). Representations of Markov processes as Multiparameter time changes. Ann. Probab. 8, 682-715.
16. MAGLAPERIDZE, N.O., TSIGROSHVILI, Z.P. & VAN PUL, M. (1998). Goodness-of-fit tests for parametric hypothesis on the distribution of point processes. Math. Methods Statist. 7, 60-77.
17. MERZBACH, E. & NUALART, D. (1986). A characterization of the spatial Poisson process and changing time. Ann. Probab. 14, 1380-1390.
18. MEYER, P. (1971). Demonstration simplifiée d'un théorème de Knight. In Séminaire de Probabilités, V, University of Strasbourg. Lecture Notes in Math. 191, 191-195.
19. NAIR, M. (1990). Random space change for multiparameter point processes. Ann. Probab. 18, 1222-1231.
20. OGATA, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes. J. Amer. Statist. Assoc. 83, 9-27.
21. OGATA, Y. (1992). Detection of precursory relative quiescence before great earthquakes through a statistical model. J. Geophys. Res. 97, 19845-19871.
22. OGATA, Y. (2001). Increased probability of large earthquakes near aftershock regions with relative quiescence. J. Geophys. Res. 106(B5), 8729-8744.
23. PAPANGELOU, F. (1972). Integrability of expected increments of point processes and a related random change of scale. Trans. Amer. Math. Soc. 165, 483-506.
24. SCHOENBERG, F. (1997). Assessment of Multi-dimensional Point Processes. PhD Dissertation, University of California, Berkeley.
25. SCHOENBERG, F. (1999). Transforming spatial point processes into Poisson processes. Stochastic Process. Appl. 81, 155-164.
26. SCHOENBERG, F.P. (2002). On rescaled Poisson processes and the Brownian bridge. Ann. Inst. Statist. Math. 54, 445-457.