0000000000077123
AUTHOR
Frederic Paik Schoenberg
Discussion of "modern statistics of spatial point processes"
The paper ‘Modern statistics for spatial point processes' by Jesper Møller and Rasmus P. Waagepetersen is based on a special invited lecture given by the authors at the 21st Nordic Conference on Mathematical Statistics, held at Rebild, Denmark, in June 2006. At the conference, Antti Penttinen and Eva B. Vedel Jensen were invited to discuss the paper. We here present the comments from the two invited discussants and from a number of other scholars, as well as the authors' responses to these comments. Below Figure 1, Figure 2, etc., refer to figures in the paper under discussion, while Figure A, Figure B, etc., refer to figures in the current discussion. All numbered sections and formulas ref…
Point process diagnostics based on weighted second-order statistics and their asymptotic properties
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.