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Statistica Sinica 18(2008), 1375-1393





NONPARAMETRIC BOOTSTRAP FOR $\mbox{\boldmath $K$}$-FUNCTIONS

ARISING FROM MIXED-EFFECTS MODELS WITH

APPLICATIONS IN NEUROPATHOLOGY


Sabine Landau and Ian P. Everall


King's College London and University of California, San Diego
Abstract: Neuropathological studies frequently determine the positions of cells on multiple brain tissue sections taken from multiple individuals. Interest arises in group comparisons of the spatial dependencies between cells, in particular the spatial dependencies of a single cell type (clustering or regularity as measured by the univariate $K$-function), or the spatial interaction of two different cell types (attraction or repulsion as measured by the bivariate $K$-function). While the nonparametric statistical analysis of spatial dependencies in the one-way design is fairly well-established, investigations often employ more complex designs. In this paper we develop a residual bootstrapping approach for $K$-functions arising from a general repeated measures design by assuming an underlying linear mixed-effects model. We illustrate our methodology by re-analysing the spatial interaction between neurons and astrocytes (brain cells that are functionally related to neurons) in a study of HIV associated dementia.



Key words and phrases: Bivariate point process, bootstrap, K-function, mixed-effects model, neuropathology, nonstationarity, replicated spatial point pattern.

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