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Abstract:
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We introduce new variance estimation procedures for second-order statistics that are computed from a single realization of intensity reweighted stationary spatial point processes. The statistics are defined either on a subset B of the observation window or on the whole window. For the former, we use sub-blocks that have the same size and shape as B as `replicates' of B in order to estimate the target variance. For the latter, we develop a subsampling estimator for a key component in the target variance and estimate its other components by method-of-moment methods. Under some suitable conditions, we prove that the proposed variance estimators are consistent for the target variances in both cases. Simulations and an application to a real data example are used to demonstrate the usefulness of the proposed methods.
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