Abstract
A diagnostic method for space–time point process is here introduced and applied to seismic data of a fixed area of Japan. Nonparametric methods are used to estimate the intensity function of a particular space–time point process and on the basis of the proposed diagnostic method, second-order features of data are analyzed: this approach seems to be useful to interpret space–time variations of the observed seismic activity and to focus on its clustering features.
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References
Adelfio, G., & Schoenberg, F. P. (2008). Point process diagnostics based on weighted second-order statistics and their asymptotic properties. Annals of the Institute of Statistical Mathematics. doi:10.1007/s10463-008-0177-1.
Baddeley, A. J., & Silverman, B. W. (1984). A cautionary example on the use of secondorder methods for analyzing point patterns. Biometrics, 40, 1089–1093.
Daley, D. J., & Vere-Jones, D. (2003). An introduction to the theory of point processes (2nd edition). New York: Springer.
Denker, M., & Keller, G. (1986). Rigorous statistical procedures for data from dynamical systems. Journal of Statistical Physics, 44, 67–94.
Diggle, P. J. (1983). Statistical analysis of spatial point patterns. London: Academic.
Gutenberg, B., & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34, 185–188.
Meyer, P. (1971). Demonstration simplifee dun theoreme de knight. In Seminaire de Probabilites V Universite de Strasbourg. Lecture Notes in Mathematics (Vol. 191, pp. 191–195). Berlin: Springer.
Ogata, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes. Journal of the American Statistical Association, 83(401), 9–27.
Ogata, Y. (1998). Space–time point-process models for earthquake occurrences. Annals of the Institute of Statistical Mathematics, 50(2), 379–402.
Schoenberg, F. P. (2003). Multi-dimensional residual analysis of point process models for earthquake occurrences. Journal American Statistical Association, 98(464), 789–795.
Silverman, B. W. (1986). Density estimation for statistics and data analysis. London: Chapman and Hall.
Utsu, T. (1961). A statistical study on the occurrence of aftershocks. Geophysical Magazine, 30, 521–605.
Veen, A., & Schoenberg, F. P. (2005). Assessing spatial point process models using weighted K-functions: Analysis of California earthquakes. In A. Baddeley, P. Gregori, J. Mateu, R. Stoica, & D. Stoyan (Eds.), Case studies in spatial point process models (pp. 293–306). New York: Springer.
Zhuang, J., Ogata, Y., & Vere-Jones, D. (2002). Stochastic declustering of space–time earthquake occurrences. Journal of the American Statistical Association, 97(458), 369–379.
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Adelfio, G. (2010). An Analysis of Earthquakes Clustering Based on a Second-Order Diagnostic Approach. In: Palumbo, F., Lauro, C., Greenacre, M. (eds) Data Analysis and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03739-9_35
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DOI: https://doi.org/10.1007/978-3-642-03739-9_35
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