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On Nonparametric Variance Estimation for Second-Order Statistics of Inhomogeneous Spatial Point Processes With a Known Parametric Intensity Form.

ABSTRACT: 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 subblocks 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. This article has supplemental material online.

SUBMITTER: Guan Y

PROVIDER: S-EPMC2844672 | biostudies-literature | 2009 Dec

REPOSITORIES: biostudies-literature

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On Nonparametric Variance Estimation for Second-Order Statistics of Inhomogeneous Spatial Point Processes With a Known Parametric Intensity Form.

Guan Yongtao Y

Journal of the American Statistical Association 20091201 488

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 subblocks 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 va ...[more]

PMID: 20336182

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