Pseudo-spectra of multivariate inhomogeneous spatial point processes Article Swipe
Qing-Ping Ding
,
Junho Yang
,
Joonho Shin
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2502.09948
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2502.09948
In this article, we propose a spectral method for a class of multivariate inhomogeneous spatial point processes, namely the second-order intensity reweighted stationary processes. A key ingredient of our approach is utilizing the asymptotic behavior of the periodogram. For second-order stationary point processes, the periodogram is an asymptotically unbiased estimator of the spectrum. By calculating the moment, we show that under inhomogeneity, the expectation of the periodogram converges to a matrix-valued function, which we refer to as the pseudo-spectrum. The pseudo-spectrum shares similar properties with the spectrum of stationary processes and admits interpretation in terms of local parameters. We derive a consistent nonparametric estimator of the pseudo-spectrum via kernel smoothing and propose two bandwidth selection methods. The performance and utility of the proposed methods are demonstrated through simulation studies and an application to rainforest point pattern data.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2502.09948
- https://arxiv.org/pdf/2502.09948
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4407632455
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Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4407632455Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2502.09948Digital Object Identifier
- Title
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Pseudo-spectra of multivariate inhomogeneous spatial point processesWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2025Year of publication
- Publication date
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2025-02-14Full publication date if available
- Authors
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Qing-Ping Ding, Junho Yang, Joonho ShinList of authors in order
- Landing page
-
https://arxiv.org/abs/2502.09948Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2502.09948Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2502.09948Direct OA link when available
- Concepts
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Multivariate statistics, Point (geometry), Spectral line, Geography, Mathematics, Statistical physics, Environmental science, Physics, Statistics, Geometry, AstronomyTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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