Some Distance-Based Tests of Independence for Sparsely-Sampled Multivariate Spatial Point Patterns

Summary Methods for the statistical analysis of spatial point patterns can be divided into two categories, according to whether or not a complete map of the underlying pattern is available. This paper is concerned only with methods for the analysis of data extracted from a pattern in situ by a 'sparse sampling' method involving the measurement of distances from sampling origins to neighbouring points of the pattern. The paper first gives a brief review of sparse sampling methods for univariate patterns and then discusses the problem of testing for independence between two or more patterns. Some new tests are described and power comparisons are presented. The methods are illustrated on two sets of forestry data, where the patterns are formed by the locations of trees of different species.