Work

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

Year: 2009

Type: article

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.

Source: Journal of the American Statistical Association

DOI: 10.1198/jasa.2009.tm08541

Author: Yongtao Guan

Institution: Yale University

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Institute of Dental and Craniofacial Research

Award: G1422009276