New Zealand Statistical Association 2024 Conference

Bethany Macdonald

University of Otago

Improving minimum contrast for clustered processes

This is joint work with Tilman Davies, Martin Hazelton

Spatial point patterns can arise from a vast array of application areas including epidemiology, ecology and geoscience. Of special interest are clustered processes, such as the log-Gaussian Cox process and Neyman-Scott processes. In such models we are interested in estimation of the 'cluster' parameters which describe the behaviour between points.

Minimum contrast is a popular estimation method for cluster processes and related models where exact likelihood based methods are unavailable. This procedure is essentially a method of moments, which involves minimising the differences between a theoretical summary statistic and its non-parametric equivalent. The pair correlation function (PCF) is a popular choice for the summary statistic and is typically estimated using kernel smoothing. However, the kernel estimate is not an unbiased estimator for the theoretical PCF and leads to biased parameter estimates. Additionally, the empirical estimate must be scaled by the squared intensity which is unknown and replaced by an estimator. For clustered processes, the standard estimator introduces further bias. We present a number of improvements to the minimum contrast procedure for clustered processes.