115
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Gamma Kernel Intensity Estimation in Temporal Point Processes

, &
Pages 1146-1162 | Received 27 Jul 2010, Accepted 04 Feb 2011, Published online: 18 Apr 2011

References

  • Adelfio , G. ( 2010 ). Kernel estimation and display of a five-dimensional conditional intensity function . Nonlinear Processes in Geophysics 17 : 237 – 244 .
  • Adelfio , G. , Chiodi , M. ( 2009 ). Second-order diagnostics for space-time point processes with application to seismic events . Environmetrics 20 : 895 – 911 .
  • Adelfio , G. , Chiodi , M. ( 2011 ). Kernel intensity for space-time point processes with application to seismological problems. In: Classification and Multivariate Analysis for Complex Data Structures. Series: Studies in Classification, Data Analysis, and Knowledge Organization. Heidelberg: Springer-Verlag, pp. 401–408 .
  • Adelfio , G. , Ogata , Y. ( 2010 ). Hybrid kernel estimates of space-time earthquake occurrance rates using the etas model . Annals of the Institute of Statistical Mathematics 62 : 127 – 143 .
  • Adelfio , G. , Chiodi , M. , De Luca , L. , Luzio , D. (2006). Nonparametric clustering of seismic events. In: Data Analysis, Classification and the Forward Search . Series : Studies in Classification, Data Analysis, and Knowledge Organization. Heidelberg: Springer-Verlag, pp. 397–404.
  • Adelfio , G. , Chiodi , M. , De Luca , L. , Luzio , D. ( 2010 ). An algorithm for earthquake clustering based on maximum likelihood . In: Data Analysis and Classification . Series: Studies in Classification, Data Analysis, and Knowledge Organization . New York : Springer , pp. 25 – 32 .
  • Bouezmarni , T. , Scaillet , O. ( 2005 ). Consistency of asymmetric kernel density estimators and smoothed histograms with application to income data. Technical Report 0306, Interuniversity Attraction Pole . Economic Theory 21 : 390 – 412 .
  • Bowman , A. W. , Hall , P. , Titterington , D. M. ( 1984 ). Cross-validation in nonparametric estimation of probabilities and probability density . Biometrika Trust 71 : 341 – 351 .
  • Chen , S. X. ( 2000 ). Probability density function estimating using gamma kernels . Annals of the Institute of Statistical Mathematics 52 : 471 – 480 .
  • Choi , E. , Hall , P. ( 1998 ). On bias reduction in local linear smoothing . Biometrika 85 ( 2 ): 333 – 345 .
  • Chow , Y. S. , German , S. , Wu , L. D. ( 1983 ). Consistent cross-validated density estimation . The Annals of Statistics 11 : 25 – 38 .
  • Daley , D. J. , Vere-Jones , D. ( 2003 ). An Introduction to the Theory of Point Processes. , 2nd ed. New York : Springer-Verlag .
  • Hall , P. ( 1982 ). Cross-validation in density estimation . Biometrika 69 ( 2 ): 383 – 390 .
  • Hall , P. ( 1983 ). Large samples optimality of least squares cross-validation in density estimation . The Annals of Statistics 11 : 1156 – 74 .
  • Hall , P. , Marron , J. S. ( 1987 ). Extent to which least-squares cross-validation minimizes integrated squared error in nonparametric density estimation . Probability Theory Related Fields 74 : 567 – 581 .
  • Jackson , D. D. , Kagan , Y. Y. ( 1999 ). Testable earthquake forecasts for 1999 . Seismlogical Research Letters 70 : 393 – 403 .
  • Ogata , Y. ( 1998 ). Space-time point-process models for earthquake occurrences . Annals of the Institute of Statistical Mathematics 50 ( 2 ): 379 – 402 .
  • Ogata , Y. , Zhuang , J. ( 2006 ). Space-time etas model and an improved extension . Tectonophysics 413 : 13 – 23 .
  • Rosenblatt , M. ( 21956 ). Remarks on some nonparametric estimates of a density function . Annals of Mathematical Statistics 27 : 832 – 837 .
  • Rudemo , M. ( 1982 ). Empirical choice of histograms and kernel density estimators . Scandinavian Journal of Statistics 9 : 65 – 78 .
  • 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. ( 1978 ). Choosing the window width when estimating a density . Biometrika Trust 65 : 1 – 11 .
  • Silverman , B. W. ( 1986 ). Density Estimation for Statistics and Data Analysis . London : Chapman and Hall .
  • Stone , C. J. ( 1984 ). An asymptotically optimal window selection rule for kernel density estimates . The Annals of Statistics 12 : 1285 – 1297 .
  • 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 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.