Properties of residuals for spatial point processes

Annals of the Institute of Statistical Mathematics

Volumn 60, Issue 3, 2008, Pages 627-649

  Baddeley, A ^a,b   Moller J ^c   Pakes, A G ^a  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^b CSIRO   (Australia)

^c AALBORG UNIVERSITY   (Denmark)

Author keywords

Distributional equivalence; Georgii Nguyen Zessin formula; Gibbs point process; Papangelou conditional intensity; Pearson residuals; Scan statistic; Set indexed martingale; Smoothed residual field

Indexed keywords

DISTRIBUTIONAL EQUIVALENCE; GEORGII-NGUYEN-ZESSIN FORMULA; GIBBS POINT PROCESS; PAPANGELOU CONDITIONAL INTENSITY; PEARSON RESIDUALS; POINT PROCESSES; SCAN STATISTIC; SET-INDEXED MARTINGALE; SMOOTHED RESIDUAL FIELD;

EID: 49149122713     PISSN: 00203157     EISSN: 15729052     Source Type: Journal    
DOI: 10.1007/s10463-007-0116-6     Document Type: Article

References (27)

1. S. Alm 1988 Approximation and simulation of the distributions of scan statistics for Poisson processes in higher dimensions Extremes 1 1 111 126
2. Andersen P., Borgan Ø., Gill R., Keiding N. (1993). Statistical Models based on Counting Processes. New York, Springer
3. Atkinson A. (1985). Plots, Transformations and Regression. Number 1 in Oxford Statistical Science Series. Clarendon, Oxford University Press
4. A. Baddeley R. Turner J. Møller M. Hazelton 2005 Residual analysis for spatial point processes (with discussion) Journal of the Royal Statistical Society, Series B 67 5 617 666
5. Brillinger D. (1978). Comparative aspects of the study of ordinary time series and of point processes. In: Krishnaiah P.(ed) Developments in Statistics. NewYork, Academic Press, pp. 33-133
6. D. Brillinger 1994 Time series, point processes, and hybrids Canadian Journal of Statistics 22 177 206
7. D. Brillinger J. Segundo 1979 Empirical examination of the threshold model of neuron firing Biological Cybernetics 35 213 220
8. Daley D., Vere-Jones D. (1988). An Introduction to the Theory of Point Processes. New York, Springer
9. Feller, W. (1971). An Introduction to Probability Theory and its Applications, volume 2. New York: John Wiley and Sons, second edition.
10. Fleming T., Harrington D. (1991). Counting Processes and Survival Analysis. New York, Wiley
11. H.-O. Georgii 1976 Canonical and grand canonical Gibbs states for continuum systems Communications of Mathematical Physics 48 31 51
12. Kalbfleisch J., Prentice R. (1980). The Statistical Analysis of Failure Time Data. NewYork, Wiley
13. Karr A. (1985). Point Processes and Their Statistical Inference. New York, Dekker
14. Lewis P. (1972). Recent results in the statistical analysis of univariate point processes. In: Lewis P.(ed) Stochastic Point Processes. New York, Wiley, pp. 1-54
15. Møller J., Waagepetersen R. (2003). Statistical Inference and Simulation for Spatial Point Processes. Boca Raton, Chapman and Hall/CRC
16. Møller, J. Waagepetersen, R. (2007). Modern spatial point process modelling and inference. Scandinavian Journal of Statistics. (To appear).
17. X Nguyen H. Zessin 1979 Integral and differential characterizations of Gibbs processes Mathematische Nachrichten 88 105 115
18. Y. Ogata 1988 Statistical models for earthquake occurrences and residual analysis for point processes Journal of the American Statistical Association 83 9 27
19. Y. Ogata K. Katsura M. Tanemura 2003 Modelling heterogeneous space-time occurrences of earthquakes and its residual analysis Applied Statistics 52 4 499 509
20. F. Papangelou 1974 The conditional intensity of general point processes and an application to line processes Zeitschrift fuer Wahscheinlichkeitstheorie und verwandte Gebiete 28 207 226
21. Preston C, (1976). Random Fields. New York, Springer
22. B. Ripley F. Kelly 1977 Markov point processes Journal of the London Mathematical Society 15 188 192
23. Ruelle D. (1969). Statistical Mechanics. New York, Wiley
24. D. Stoyan P. Grabarnik 1991 Second-order characteristics for stochastic structures connected with Gibbs point processes Mathematische Nachrichten 151 95 100
25. L. Takács 1955 On stochastic processes connected with certain physical recording apparatuses Acta Mathematica Academiae Scientiarum Hungaricae 6 363 374
26. W. Vervaat 1979 On a stochastic difference equation and a representation of non-negative infinitely divisible random variables Advances in Applied Probability 11 750 783
27. Zhuang J., Ogata Y., Vere-Jones D. (2005). Diagnostic analysis of space-time branching processes for earthquakes. In Baddeley A., Gregori P., Mateu J., Stoica R., Stoyan D., (eds) Case Studies in Spatial Point Process Modelling, number 185 in Lecture Notes in Statistics, chapter 15. New York: Springer