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 supplementary material online.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1482-1491 |
| Number of pages | 10 |
| Journal | Journal of the American Statistical Association |
| Volume | 104 |
| Issue number | 488 |
| DOIs | |
| State | Published - Dec 2009 |
| Externally published | Yes |
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Keywords
- Intensity reweighted stationary processes
- Second-order statistics
- Variance estimation
ASJC Scopus subject areas
- Statistics, Probability and Uncertainty
- Statistics and Probability
Cite this
On nonparametric variance estimation for second-order statistics of inhomogeneous spatial point processes with a known parametric intensity form. / Guan, Yongtao.
In: Journal of the American Statistical Association, Vol. 104, No. 488, 12.2009, p. 1482-1491.Research output: Contribution to journal › Article
}
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
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
UR - http://www.scopus.com/inward/record.url?scp=74049151068&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=74049151068&partnerID=8YFLogxK
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 -