Consistent parametric estimation of the intensity of a spatial-temporal point process

Journal of Statistical Planning and Inference

Volumn 128, Issue 1, 2005, Pages 79-93

  Schoenberg, Frederic Paik ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Conditional intensity; Consistency; Intensity function; Maximum likelihood estimation; Poisson process; Weighted least squares estimation

Indexed keywords

EID: 15344348023     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2003.09.027     Document Type: Article

References (29)

1. Abramowitz M. Abramowitz M. Stegun I. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables 1964 US Government Printing Office Washington DC
2. Andersen P.K. Borgan O. Gill R.D. Keiding N. Statistical Models Based on Counting Processes 1993 Springer New York
3. Brémaud P. Point Processes and Queues 1981 Springer New York
4. Brillinger D.R. Statistical inference for stationary point processes Stochastic Process. Related Topics 1 1975 55-99
5. Brillinger, D.R., 1998. Some wavelet analyses of point process data. In: Proceedings of the 31st Asilomar Conference on Signals, Systems and Computers. IEEE Computer Society, Los Alamitos, CA, pp. 1087-1091.
6. Cox D.R. Lewis P.A.W. The Statistical Analysis of Series of Events 1966 Methuen London
7. Daley D. Vere-Jones D. An Introduction to the Theory of Point Processes 1988 Springer New York
8. Helmers R. Zitikis R. On estimation of Poisson intensity functions Ann. Inst. Statist. Math. 51 1999 265-280
9. Helmers R. Mangku W. Zitikis R. Consistent estimation of cyclic Poisson intensity functions J. Multivariate Anal. 84 2003 19-39
10. Huang F. Ogata Y. Improvements of the maximum pseudo-likelihood estimators in various spatial statistical models J. Comput. Graph Statist. 8 1999 510-530
11. Isham V. Westcott M. A self-correcting point process Stochastic Process Appl. 8 1979 335-347
12. Jensen J.L. Asymptotic normality of estimates in spatial point processes Scand. J. Statist. 20 1993 97-109
13. Karr A.F. Point Processes and their Statistical Inference 1986 Marcel Dekker New York
14. Krickeberg K. Processus ponctuels en statistique Hennequin P.L. Ecole d'Eté de Probabilités de Saint-Flour X 1982 205-313 International Cooperative Publishing House Fairland, MD
15. Kutoyants Y.A. Parameter Estimation for Stochastic Processes 1984 Heldermann Verlag Berlin
16. Nishiyama Y. Local asymptotic normality of a sequential model for market point processes and its applications Ann. Inst. Statist. Math. 47 1995 195-209
17. Ogata Y. The asymptotic behaviour of maximum likelihood estimators for stationary point processes Ann. Inst. Statist. Math. 30 1978 243-261
18. Ogata Y. Space-time point process models for earthquake occurrences Ann. Inst. Statist. Math. 50 1998 379-402
19. Ogata Y. Vere-Jones D. Inference for earthquake models: A self-correcting model Stochastic Process Appl. 17 1984 337-347
20. Ogata, Y., Katsura, K., Tanemura, M., 2001. Modelling of heterogeneous space-time seismic activity and its residual analysis. Research Memorandum 808, Institute of Statistical Mathematics.
21. Peng, R.D., 2003. Applications of multi-dimensional point process methodology to wildfire hazard assessment. Ph.D. Thesis, Department of Statistics, University of California, Los Angeles.
22. Rathbun S.L. Asymptotic properties of the maximum likelihood estimator for spatio-temporal point processes J. Statist. Plann. Inference 51 1996 55-74
23. Rathbun S.L. Estimation of Poisson intensity using partially observed concomitant variables Biometrics 52 1996 226-242
24. Rathbun S.L. Cressie N. Asymptotic properties of estimators for the parameters of spatial inhomogeneous Poisson point processes Adv. Appl. Probab. 26 1994 122-154
25. Rudin W. Principles of Mathematical Analysis 3rd Edition 1976 McGraw-Hill New York
26. Schoenberg, F.P., 2004. Multi-dimensional residual analysis of point process models for earthquake occurrences. J. Amer. Statist. Assoc., in press.
27. Sweeting T.J. Uniform asymptotic normality of the maximum likelihood estimator Ann. Statist. 8 1980 1375-1381
28. Vere-Jones D. Statistical methods for the description and display of earthquake catalogs Walden A. Guttorp P. Statistics in the Environmental and Earth Sciences 1992 220-236 Edward Arnold London
29. Vere-Jones D. Ogata Y. On the moments of a self-correcting process J. Appl. Probab. 21 1984 335-342