TY - JOUR

T1 - Point process diagnostics based on weighted second-order statistics and their asymptotic properties

AU - Adelfio, Giada

AU - Schoenberg, Frederic Paik

PY - 2009

Y1 - 2009

N2 - A new approach for point process diagnostics is presented. The method isbased on extending second-order statistics for point processes by weighting each pointby the inverse of the conditional intensity function at the point’s location. The resultis generalized versions of the spectral density, R/S statistic, correlation integral andK-function, which can be used to test the fit of a complex point process model withan arbitrary conditional intensity function, rather than a stationary Poisson model.Asymptotic properties of these generalized second-order statistics are derived, usingan approach based on martingale theory.

AB - A new approach for point process diagnostics is presented. The method isbased on extending second-order statistics for point processes by weighting each pointby the inverse of the conditional intensity function at the point’s location. The resultis generalized versions of the spectral density, R/S statistic, correlation integral andK-function, which can be used to test the fit of a complex point process model withan arbitrary conditional intensity function, rather than a stationary Poisson model.Asymptotic properties of these generalized second-order statistics are derived, usingan approach based on martingale theory.

KW - Residual analysis

KW - conditional
intensity function

KW - point process

KW - second-order analysis

KW - Residual analysis

KW - conditional
intensity function

KW - point process

KW - second-order analysis

UR - http://hdl.handle.net/10447/38511

M3 - Article

VL - 61

SP - 929

EP - 948

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

ER -