6533b7dcfe1ef96bd1272b2e

RESEARCH PRODUCT

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

Giada AdelfioFrederic Paik Schoenberg

subject

Statistics and ProbabilityMathematical optimizationSpectral densityInverseResidual analysis point process second-order analysis conditional intensity functionResidualPoint processWeightingCorrelation integralApplied mathematicsPoint (geometry)Settore SECS-S/01 - StatisticaStatisticMathematics

description

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

yearjournalcountryeditionlanguage
2008-04-24Annals of the Institute of Statistical Mathematics
https://doi.org/10.1007/s10463-008-0177-1