On estimating the reduced second moment measure of a stationary spatial point process

A. G. Chetwynd; P. J. Diggle

On estimating the reduced second moment measure of a stationary spatial point process

A. G. Chetwynd, P. J. Diggle

Research output: Contribution to journal › Article › peer-review

Abstract

A method is proposed for estimating the covariance structure of a nonparametric estimator for the reduced second moment measure, K(s), of a homogeneous planar Poisson process. The method relies on the invariance of the reduced second moment measure to random thinning, and the known covariance structure of the estimator under random sampling from a fixed set of points. The possible extension of the method to stationary Cox processes is discussed.

Original language	English (US)
Pages (from-to)	11-15
Number of pages	5
Journal	Australian and New Zealand Journal of Statistics
Volume	40
Issue number	1
State	Published - Mar 1998
Externally published	Yes

Keywords

Point process
Second-order analysis
Spatial statistics
Variance of estimation

ASJC Scopus subject areas

Statistics and Probability

Cite this

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abstract = "A method is proposed for estimating the covariance structure of a nonparametric estimator for the reduced second moment measure, K(s), of a homogeneous planar Poisson process. The method relies on the invariance of the reduced second moment measure to random thinning, and the known covariance structure of the estimator under random sampling from a fixed set of points. The possible extension of the method to stationary Cox processes is discussed.",

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AU - Diggle, P. J.

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N2 - A method is proposed for estimating the covariance structure of a nonparametric estimator for the reduced second moment measure, K(s), of a homogeneous planar Poisson process. The method relies on the invariance of the reduced second moment measure to random thinning, and the known covariance structure of the estimator under random sampling from a fixed set of points. The possible extension of the method to stationary Cox processes is discussed.

AB - A method is proposed for estimating the covariance structure of a nonparametric estimator for the reduced second moment measure, K(s), of a homogeneous planar Poisson process. The method relies on the invariance of the reduced second moment measure to random thinning, and the known covariance structure of the estimator under random sampling from a fixed set of points. The possible extension of the method to stationary Cox processes is discussed.

KW - Point process

KW - Second-order analysis

KW - Spatial statistics

KW - Variance of estimation

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On estimating the reduced second moment measure of a stationary spatial point process

Abstract

Keywords

ASJC Scopus subject areas

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