TY - JOUR
T1 - On nonparametric variance estimation for second-order statistics of inhomogeneous spatial point processes with a known parametric intensity form
AU - Guan, Yongtao
N1 - Funding Information:
Yongtao Guan is Assistant Professor, Division of Biostatistics, Yale University, New Haven, CT 06520-8034 (E-mail: yongtao.guan@yale.edu). Yong-tao Guan’s research was supported by NSF grants DMS-0706806 and DMS-0845368 and by NIH/NIDCR grant UL1 DE019586. The author thanks the Editor, an Associate Editor and two referees for their helpful comments that have greatly improved this manuscript.
PY - 2009/12
Y1 - 2009/12
N2 - 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 supplementary material online.
AB - 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 supplementary material online.
KW - Intensity reweighted stationary processes
KW - Second-order statistics
KW - Variance estimation
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U2 - 10.1198/jasa.2009.tm08541
DO - 10.1198/jasa.2009.tm08541
M3 - Article
AN - SCOPUS:74049151068
VL - 104
SP - 1482
EP - 1491
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
SN - 0162-1459
IS - 488
ER -