Fast Covariance Estimation for Innovations Computed from a Spatial Gibbs Point Process

• Published in: Scandinavian journal of statistics Vol. 40; no. 4; pp. 669 - 684
• Main Authors: Coeurjolly, Jean-François, Rubak, Ege
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.12.2013; Wiley Publishing; Wiley
• Subjects: Asymptotic properties; confidence intervals; Estimating techniques; exponential family models; Georgii-Nguyen-Zessin formula; innovation process; Innovations; Mathematics; maximum pseudo-likelihood; Statistical analysis; Statistical methods; Statistics; Statistics Theory; Studies; exponential family models; confidence intervals; maximum pseudo-likelihood; innovation process; Georgii-Nguyen-Zessin formula
• ISSN: 0303-6898; 1467-9469
• DOI: 10.1111/sjos.12017

In this paper, we derive an exact formula for the covariance of two innovations computed from a spatial Gibbs point process and suggest a fast method for estimating this covariance. We show how this methodology can be used to estimate the asymptotic covariance matrix of the maximum pseudo-likelihood estimator of the parameters of a spatial Gibbs point process model. This allows us to construct asymptotic confidence intervals for the parameters. We illustrate the efficiency of our procedure in a simulation study for several classical parametric models. The procedure is implemented in the statistical software R, and it is included in spatstat, which is an R package for analyzing spatial point patterns.