Non‑parametric adaptive bandwidth selection for kernel estimators of spatial intensity functions

Marie-Colette van Lieshout

doi:10.1007/s10463-023-00890-6

Non‑parametric adaptive bandwidth selection for kernel estimators of spatial intensity functions

Marie-Colette van Lieshout

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

1 Citation (Scopus)

17 Downloads (Pure)

Abstract

We introduce a new fully non-parametric two-step adaptive bandwidth selection method for kernel estimators of spatial point process intensity functions based on the Campbell–Mecke formula and Abramson’s square root law. We present a simulation study to assess its performance relative to other adaptive and global bandwidth selectors, investigate the influence of the pilot estimator and apply the technique to two data sets: A pattern of trees and an earthquake catalogue.

Original language	English
Pages (from-to)	313–331
Number of pages	19
Journal	Annals of the Institute of Statistical Mathematics
Volume	76
Early online date	22 Dec 2023
DOIs	https://doi.org/10.1007/s10463-023-00890-6
Publication status	Published - Apr 2024

Keywords

2024 OA procedure
Bandwidth selection
Campbell–Mecke formula
Intensity function
Poisson leave-one-out cross-validation log likelihood
Point process
Adaptive kernel estimation

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10.1007/s10463-023-00890-6

2024-XLieshout_10463-023-00890-6Final published version, 1.73 MBLicence: Taverne

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1 Preprint

Non-parametric adaptive bandwidth selection for kernel estimators of spatial intensity functions
van Lieshout, M.-C., 21 Oct 2022, ArXiv.org, p. 1-11, 11 p.
Research output: Working paper › Preprint › Academic

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Cite this

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title = "Non‑parametric adaptive bandwidth selection for kernel estimators of spatial intensity functions",

abstract = "We introduce a new fully non-parametric two-step adaptive bandwidth selection method for kernel estimators of spatial point process intensity functions based on the Campbell–Mecke formula and Abramson{\textquoteright}s square root law. We present a simulation study to assess its performance relative to other adaptive and global bandwidth selectors, investigate the influence of the pilot estimator and apply the technique to two data sets: A pattern of trees and an earthquake catalogue.",

keywords = "2024 OA procedure, Bandwidth selection, Campbell–Mecke formula, Intensity function, Poisson leave-one-out cross-validation log likelihood, Point process, Adaptive kernel estimation",

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AB - We introduce a new fully non-parametric two-step adaptive bandwidth selection method for kernel estimators of spatial point process intensity functions based on the Campbell–Mecke formula and Abramson’s square root law. We present a simulation study to assess its performance relative to other adaptive and global bandwidth selectors, investigate the influence of the pilot estimator and apply the technique to two data sets: A pattern of trees and an earthquake catalogue.

KW - 2024 OA procedure

KW - Bandwidth selection

KW - Campbell–Mecke formula

KW - Intensity function

KW - Poisson leave-one-out cross-validation log likelihood

KW - Point process

KW - Adaptive kernel estimation

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DO - 10.1007/s10463-023-00890-6

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VL - 76

SP - 313

EP - 331

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

ER -

Non‑parametric adaptive bandwidth selection for kernel estimators of spatial intensity functions

Abstract

Keywords

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Research output

Non-parametric adaptive bandwidth selection for kernel estimators of spatial intensity functions

Cite this