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The Correct Asymptotic Variance for the Sample Mean of a Homogeneous Poisson Marked Point Process

Part of: Limit theorems Special processes

Published online by Cambridge University Press:  30 January 2018

William Garner  and
Dimitris N. Politis
William Garner*
Affiliation:
University of California at San Diego
Dimitris N. Politis*
Affiliation:
University of California at San Diego
*
∗ Postal address: Department of Mathematics, University of California at San Diego, La Jolla, CA 92093, USA.
∗ Postal address: Department of Mathematics, University of California at San Diego, La Jolla, CA 92093, USA.
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Abstract

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The asymptotic variance of the sample mean of a homogeneous Poisson marked point process has been studied in the literature, but confusion has arisen as to the correct expression due to some technical intricacies. This note sets the record straight with regards to the variance of the sample mean. In addition, a central limit theorem in the general d-dimensional case is also established.

Keywords

Central limit theoremmarked point process

MSC classification

Primary: 60F05: Central limit and other weak theorems 60K99: None of the above, but in this section

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 3 , September 2013 , pp. 889 - 892
Copyright
© Applied Probability Trust 

References

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