Non-parametric confidence intervals for correlations in nearest-neighbour Markov point processes

Abstract

We study bootstrap confidence intervals for correlation functions in nearest-neighbour Markov point processes, where the neighbours are characterized by an interaction of bounded radius r. In forestry statistics, the points are tree locations belonging to a region (forest) A, and the marks are qualitative or quantitative tree variables, such as tree species, the stem diameter, crown length or tree height. Estimating and analysing correlation functions between locations and marks, cross-correlations between different species and their marks, is typically a key step in statistical interpretation of mapped data sets from a forest stand. In order to define the original sample, we propose coding schemes, which are fixed and divide the observed region A of the point process into regular, conditionally independent subregions {Bv} located at Euclidean distance d ≥ 2r. Bootstrap confidence intervals are then obtained directly, by considering kernel density estimates from all subregions {Bv} as conditionally independent replicates. Copyright © 2002 John Wiley & Sons, Ltd.