Bias correction for parameter estimates of spatial point process models

Abstract

When a spatial point process model is fitted to spatial point pattern data using standard software, the parameter estimates are typically biased. Contrary to folklore, the bias does not reflect weaknesses of the underlying mathematical methods, but is mainly due to the effects of discretization of the spatial domain. We investigate two approaches to correcting the bias: a Newton–Raphson-type correction and Richardson extrapolation. In simulation experiments, Richardson extrapolation performs best.

Keywords:

• Berman–Turner device
• composite likelihood
• discretization
• Gibbs point process
• logistic regression
• Newton–Raphson algorithm
• numerical integration
• Poisson point process
• pseudolikelihood
• Richardson extrapolation

AMS Subject Classification::

• Primary: 62M30
• Secondary: 62F10
• 65D30
• 62-07