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Volumn 51, Issue 1, 1996, Pages 55-74

Asymptotic properties of the maximum likelihood estimator for spatio-temporal point processes

Author keywords

Asymptotic normality; Consistency; Seismology; Self correcting point process; Self exciting point process

Indexed keywords


EID: 0030119979     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/0378-3758(95)00070-4     Document Type: Article
Times cited : (54)

References (38)
  • 1
    • 0001609210 scopus 로고
    • Comment on "likelihood analysis of point processes and its applications to seismological data"
    • by Y. Ogata
    • Berman, M. (1983). Comment on "Likelihood analysis of point processes and its applications to seismological data" by Y. Ogata. Bull. Internat. Statist. Inst. 50, 412-418.
    • (1983) Bull. Internat. Statist. Inst. , vol.50 , pp. 412-418
    • Berman, M.1
  • 3
    • 0023688346 scopus 로고
    • Maximum likelihood identificdation of neural point process systems
    • Chornoboy, E.S., L.P. Schramm and A.F. Karr (1988). Maximum likelihood identificdation of neural point process systems. Biol. Cybernet. 59, 265-275.
    • (1988) Biol. Cybernet. , vol.59 , pp. 265-275
    • Chornoboy, E.S.1    Schramm, L.P.2    Karr, A.F.3
  • 7
    • 0011653726 scopus 로고
    • Time reversible and Gibbsian point processes, I: Markovian spatial birth and death processes on a general phase space
    • Glötzel, E. (1981). Time reversible and Gibbsian point processes, I: Markovian spatial birth and death processes on a general phase space. Math. Nachr. 102, 217-222.
    • (1981) Math. Nachr. , vol.102 , pp. 217-222
    • Glötzel, E.1
  • 8
    • 0018654828 scopus 로고
    • A stochastic kinematic study of subsynoptic space-time rainfall
    • Gupta, V.K. and E.C. Waymire (1979). A stochastic kinematic study of subsynoptic space-time rainfall. Water Resources. Res. 15, 637-644.
    • (1979) Water Resources. Res. , vol.15 , pp. 637-644
    • Gupta, V.K.1    Waymire, E.C.2
  • 10
    • 0002920214 scopus 로고
    • Spectra of some self-exciting and mutually exciting point processes
    • Hawkes, A.G. (1971). Spectra of some self-exciting and mutually exciting point processes. Biometrika 58, 83-90.
    • (1971) Biometrika , vol.58 , pp. 83-90
    • Hawkes, A.G.1
  • 11
    • 0001446567 scopus 로고
    • A cluster processes representation of a self-exciting process
    • Hawkes, A.G. and D. Oakes (1974). A cluster processes representation of a self-exciting process. J Appl. Probab. 11, 493-503.
    • (1974) J Appl. Probab. , vol.11 , pp. 493-503
    • Hawkes, A.G.1    Oakes, D.2
  • 12
    • 0011672968 scopus 로고
    • Modelling of clustering effects in point processes: An application to failures in SPC-systems
    • Helvik, B.E. and A.R. Swensen (1987). Modelling of clustering effects in point processes: an application to failures in SPC-systems. Scand. J. Statist. 14, 57-66.
    • (1987) Scand. J. Statist. , vol.14 , pp. 57-66
    • Helvik, B.E.1    Swensen, A.R.2
  • 18
    • 0011671120 scopus 로고
    • Asymptotic properties and equilibrium conditions for branching poisson processes
    • Lewis, P.A.W. (1969). Asymptotic properties and equilibrium conditions for branching Poisson processes. J. Appl. Probab. 6, 355-371.
    • (1969) J. Appl. Probab. , vol.6 , pp. 355-371
    • Lewis, P.A.W.1
  • 19
    • 0011606946 scopus 로고
    • Uniform LAN condition of planar Gibbsian point processes and optimality of maximum likelihood estimators of soft-core potential functions
    • Mase, S. (1992). Uniform LAN condition of planar Gibbsian point processes and optimality of maximum likelihood estimators of soft-core potential functions. Prob. Theory Related Fields 92, 51-67.
    • (1992) Prob. Theory Related Fields , vol.92 , pp. 51-67
    • Mase, S.1
  • 20
    • 0003154052 scopus 로고
    • Statistical approach to problems of cosmology
    • Neyman, J. and E.L. Scott (1958). Statistical approach to problems of cosmology. J. Roy. Statist. Soc. B 20, 1-43.
    • (1958) J. Roy. Statist. Soc. B , vol.20 , pp. 1-43
    • Neyman, J.1    Scott, E.L.2
  • 21
    • 51249182136 scopus 로고
    • The asymptotic behavior of maximum likelihood estimators for stationary point processes
    • Ogata, Y. (1978). The asymptotic behavior of maximum likelihood estimators for stationary point processes. Ann. Inst. Statist. Math. 30A, 243-261.
    • (1978) Ann. Inst. Statist. Math. , vol.30 A , pp. 243-261
    • Ogata, Y.1
  • 22
    • 0020969023 scopus 로고
    • Estimation of the parameters in the modified Omori formula for aftershock frequencies by the maximum likelihood procedure
    • Ogata, Y. (1983). Estimation of the parameters in the modified Omori formula for aftershock frequencies by the maximum likelihood procedure. J. Phys. Earth 31, 115-124.
    • (1983) J. Phys. Earth , vol.31 , pp. 115-124
    • Ogata, Y.1
  • 23
    • 0012346731 scopus 로고
    • Statistical models for earthquake occurrences and residual analysis for point processes
    • Ogata, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes. J. Amer. Statist. Assoc. 83, 9-27.
    • (1988) J. Amer. Statist. Assoc. , vol.83 , pp. 9-27
    • Ogata, Y.1
  • 24
    • 0011675938 scopus 로고
    • Space-time modeling of earthquake occurrences
    • Ogata, Y. (1993). Space-time modeling of earthquake occurrences. Bull. Internat. Statist. Inst. 55, 249-250.
    • (1993) Bull. Internat. Statist. Inst. , vol.55 , pp. 249-250
    • Ogata, Y.1
  • 25
    • 51249184296 scopus 로고
    • The application of linear intensity models to the investigation of causal relations between a point process and another stochastic process
    • Ogata, Y., H. Akaike and K. Katsura (1982). The application of linear intensity models to the investigation of causal relations between a point process and another stochastic process. Ann. Inst. Statist. Math. 34B, 373-387.
    • (1982) Ann. Inst. Statist. Math. , vol.34 B , pp. 373-387
    • Ogata, Y.1    Akaike, H.2    Katsura, K.3
  • 26
    • 0001703940 scopus 로고
    • Point-process models with linearly parametrized intensity for application to earthquake data
    • Ogata, Y. and K. Katsura (1986). Point-process models with linearly parametrized intensity for application to earthquake data. J. Appl. Probab. 23A, 291-310.
    • (1986) J. Appl. Probab. , vol.23 A , pp. 291-310
    • Ogata, Y.1    Katsura, K.2
  • 27
    • 84980187341 scopus 로고
    • One second-order and orientation analysis of planar stationary point proceses
    • Ohser, J. and D. Stoyan (1981). One second-order and orientation analysis of planar stationary point proceses. Biometrical J. 23, 523-533.
    • (1981) Biometrical J. , vol.23 , pp. 523-533
    • Ohser, J.1    Stoyan, D.2
  • 29
    • 0001606746 scopus 로고
    • Modeling marked spatio-temporal point processes
    • Rathbun, S.L. (1993). Modeling marked spatio-temporal point processes. Bull. Internat. Statist. Inst. 55, 379-396.
    • (1993) Bull. Internat. Statist. Inst. , vol.55 , pp. 379-396
    • Rathbun, S.L.1
  • 30
    • 0000949943 scopus 로고
    • Asymptotic properties of estimators for the parameters of spatial inhomogeneous poisson point processes
    • Rathbun, S.L. and N. Cressie (1994) Asymptotic properties of estimators for the parameters of spatial inhomogeneous Poisson point processes. Adv. Appl. Probab. 26, 122-154.
    • (1994) Adv. Appl. Probab. , vol.26 , pp. 122-154
    • Rathbun, S.L.1    Cressie, N.2
  • 31
    • 0000135848 scopus 로고
    • Modeling spatial patterns
    • Ripley, B.D. (1977). Modeling spatial patterns. J. Roy. Statist. Soc. B 39, 172-192.
    • (1977) J. Roy. Statist. Soc. B , vol.39 , pp. 172-192
    • Ripley, B.D.1
  • 32
    • 0023524174 scopus 로고
    • Mathematical models of rainstorm events in time and space
    • Rodriguez-Iturbe, I. and P.S. Eagleson (1987). Mathematical models of rainstorm events in time and space. Water Resources Res. 23, 181-190.
    • (1987) Water Resources Res. , vol.23 , pp. 181-190
    • Rodriguez-Iturbe, I.1    Eagleson, P.S.2
  • 33
    • 0022167565 scopus 로고
    • Parameter estimation for a model of space-time rainfall
    • Smith, J.A. and A.F. Karr (1985). Parameter estimation for a model of space-time rainfall. Water Resources Res. 21, 1251-1257.
    • (1985) Water Resources Res. , vol.21 , pp. 1251-1257
    • Smith, J.A.1    Karr, A.F.2
  • 34
    • 0018632772 scopus 로고
    • Interrupted point processes
    • Stoyan, D. (1979) Interrupted point processes. Biometrical J. 21, 607-610.
    • (1979) Biometrical J. , vol.21 , pp. 607-610
    • Stoyan, D.1
  • 35
    • 0000844245 scopus 로고
    • Uniform asymptotic normality of the maximum likelihood estimator
    • Sweeting, T.J. (1980). Uniform asymptotic normality of the maximum likelihood estimator. Ann. Statist. 8, 1375-1381.
    • (1980) Ann. Statist. , vol.8 , pp. 1375-1381
    • Sweeting, T.J.1
  • 36
    • 0021450810 scopus 로고
    • On the moments of a self-correcting process
    • Vere-Jones, D. and Y. Ogata (1984). On the moments of a self-correcting process. J. Appl. Probab. 21, 335-342.
    • (1984) J. Appl. Probab. , vol.21 , pp. 335-342
    • Vere-Jones, D.1    Ogata, Y.2
  • 37
    • 0021641436 scopus 로고
    • A spectral theory of rainfall intensity at the meso-β scale
    • Waymire, E., V.K. Gupta and I. Rodriguez-Iturbe (1984). A spectral theory of rainfall intensity at the meso-β scale. Water Resources Res. 20, 1453-1465.
    • (1984) Water Resources Res. , vol.20 , pp. 1453-1465
    • Waymire, E.1    Gupta, V.K.2    Rodriguez-Iturbe, I.3
  • 38
    • 0008599531 scopus 로고
    • The probability generating functional
    • Westcott, M. (1972). The probability generating functional. J. Austral. Math. Soc. 14, 448-466.
    • (1972) J. Austral. Math. Soc. , vol.14 , pp. 448-466
    • Westcott, M.1


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