Recursive Estimation of the Intensity Function of the Non-homogeneous Poisson Process

Marcel Sihintoe Badiane; Siba Kalivogui; Bakary D Coulibaly; Aguemon Wiwegnon Uriel-Longin

doi:doi:10.11648/j.ajtas.20251406.12

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Recursive Estimation of the Intensity Function of the Non-homogeneous Poisson Process

Marcel Sihintoe Badiane^*, Siba Kalivogui, Bakary D Coulibaly, Aguemon Wiwegnon Uriel-Longin

Published in American Journal of Theoretical and Applied Statistics (Volume 14, Issue 6)

Received: 7 October 2025 Accepted: 25 October 2025 Published: 19 December 2025

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Abstract

This study focuses on the recursive nonparametric estimation of the intensity function associated with a nonhomogeneous Poisson process. Accurately estimating the intensity function is crucial for understanding the dynamics of events in fields such as finance, neuroscience, and environmental monitoring. While traditional nonparametric estimators are theoretically robust, their reliance on the entire dataset for every update makes them impractical for real-time applications. To overcome this limitation, we introduce a recursive estimator that supports efficient, online updates as new data becomes available. This approach significantly lowers computational overhead while maintaining strong statistical reliability. We thoroughly analyze the asymptotic behavior of the proposed estimator, paying particular attention to the Asymptotic Mean Integrated Squared Error (AMISE), a key measure of estimation accuracy. Additionally, we compare the performance of our recursive estimator with Cucala’s non-recursive method. The results reveal that our approach achieves equivalent or superior accuracy in terms of AMISE, particularly in large-sample scenarios. A computational performance comparison further underscores the advantages of the proposed method, demonstrating its substantial reduction in execution time and its suitability for applications requiring rapid processing.

Published in	American Journal of Theoretical and Applied Statistics (Volume 14, Issue 6)
DOI	10.11648/j.ajtas.20251406.12
Page(s)	267-276
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Nonparametric Estimation, Recursive Kernel Estimators, Intensity Function

References

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APA Style

Badiane, M. S., Kalivogui, S., Coulibaly, B. D., Uriel-Longin, A. W. (2025). Recursive Estimation of the Intensity Function of the Non-homogeneous Poisson Process. American Journal of Theoretical and Applied Statistics, 14(6), 267-276. https://doi.org/10.11648/j.ajtas.20251406.12

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ACS Style

Badiane, M. S.; Kalivogui, S.; Coulibaly, B. D.; Uriel-Longin, A. W. Recursive Estimation of the Intensity Function of the Non-homogeneous Poisson Process. Am. J. Theor. Appl. Stat. 2025, 14(6), 267-276. doi: 10.11648/j.ajtas.20251406.12

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AMA Style

Badiane MS, Kalivogui S, Coulibaly BD, Uriel-Longin AW. Recursive Estimation of the Intensity Function of the Non-homogeneous Poisson Process. Am J Theor Appl Stat. 2025;14(6):267-276. doi: 10.11648/j.ajtas.20251406.12

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@article{10.11648/j.ajtas.20251406.12,
  author = {Marcel Sihintoe Badiane and Siba Kalivogui and Bakary D Coulibaly and Aguemon Wiwegnon Uriel-Longin},
  title = {Recursive Estimation of the Intensity Function of the Non-homogeneous Poisson Process},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {14},
  number = {6},
  pages = {267-276},
  doi = {10.11648/j.ajtas.20251406.12},
  url = {https://doi.org/10.11648/j.ajtas.20251406.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20251406.12},
  abstract = {This study focuses on the recursive nonparametric estimation of the intensity function associated with a nonhomogeneous Poisson process. Accurately estimating the intensity function is crucial for understanding the dynamics of events in fields such as finance, neuroscience, and environmental monitoring. While traditional nonparametric estimators are theoretically robust, their reliance on the entire dataset for every update makes them impractical for real-time applications. To overcome this limitation, we introduce a recursive estimator that supports efficient, online updates as new data becomes available. This approach significantly lowers computational overhead while maintaining strong statistical reliability. We thoroughly analyze the asymptotic behavior of the proposed estimator, paying particular attention to the Asymptotic Mean Integrated Squared Error (AMISE), a key measure of estimation accuracy. Additionally, we compare the performance of our recursive estimator with Cucala’s non-recursive method. The results reveal that our approach achieves equivalent or superior accuracy in terms of AMISE, particularly in large-sample scenarios. A computational performance comparison further underscores the advantages of the proposed method, demonstrating its substantial reduction in execution time and its suitability for applications requiring rapid processing.
},
 year = {2025}
}

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TY  - JOUR
T1  - Recursive Estimation of the Intensity Function of the Non-homogeneous Poisson Process
AU  - Marcel Sihintoe Badiane
AU  - Siba Kalivogui
AU  - Bakary D Coulibaly
AU  - Aguemon Wiwegnon Uriel-Longin
Y1  - 2025/12/19
PY  - 2025
N1  - https://doi.org/10.11648/j.ajtas.20251406.12
DO  - 10.11648/j.ajtas.20251406.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 267
EP  - 276
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20251406.12
AB  - This study focuses on the recursive nonparametric estimation of the intensity function associated with a nonhomogeneous Poisson process. Accurately estimating the intensity function is crucial for understanding the dynamics of events in fields such as finance, neuroscience, and environmental monitoring. While traditional nonparametric estimators are theoretically robust, their reliance on the entire dataset for every update makes them impractical for real-time applications. To overcome this limitation, we introduce a recursive estimator that supports efficient, online updates as new data becomes available. This approach significantly lowers computational overhead while maintaining strong statistical reliability. We thoroughly analyze the asymptotic behavior of the proposed estimator, paying particular attention to the Asymptotic Mean Integrated Squared Error (AMISE), a key measure of estimation accuracy. Additionally, we compare the performance of our recursive estimator with Cucala’s non-recursive method. The results reveal that our approach achieves equivalent or superior accuracy in terms of AMISE, particularly in large-sample scenarios. A computational performance comparison further underscores the advantages of the proposed method, demonstrating its substantial reduction in execution time and its suitability for applications requiring rapid processing.

VL  - 14
IS  - 6
ER  -

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Author Information

Marcel Sihintoe Badiane

Department Mathematics, Kindia University Faculty of Sciences, Kindia, Guinea

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Siba Kalivogui

Department Mathematics, Kindia University Faculty of Sciences, Kindia, Guinea

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Bakary D Coulibaly

Department Mathematics, Kindia University Faculty of Sciences, Kindia, Guinea

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Aguemon Wiwegnon Uriel-Longin

Department Mathematics, Kindia University Faculty of Sciences, Kindia, Guinea

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APA Style

Badiane, M. S., Kalivogui, S., Coulibaly, B. D., Uriel-Longin, A. W. (2025). Recursive Estimation of the Intensity Function of the Non-homogeneous Poisson Process. American Journal of Theoretical and Applied Statistics, 14(6), 267-276. https://doi.org/10.11648/j.ajtas.20251406.12

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ACS Style

Badiane, M. S.; Kalivogui, S.; Coulibaly, B. D.; Uriel-Longin, A. W. Recursive Estimation of the Intensity Function of the Non-homogeneous Poisson Process. Am. J. Theor. Appl. Stat. 2025, 14(6), 267-276. doi: 10.11648/j.ajtas.20251406.12

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AMA Style

Badiane MS, Kalivogui S, Coulibaly BD, Uriel-Longin AW. Recursive Estimation of the Intensity Function of the Non-homogeneous Poisson Process. Am J Theor Appl Stat. 2025;14(6):267-276. doi: 10.11648/j.ajtas.20251406.12

Copy | Download

@article{10.11648/j.ajtas.20251406.12,
  author = {Marcel Sihintoe Badiane and Siba Kalivogui and Bakary D Coulibaly and Aguemon Wiwegnon Uriel-Longin},
  title = {Recursive Estimation of the Intensity Function of the Non-homogeneous Poisson Process},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {14},
  number = {6},
  pages = {267-276},
  doi = {10.11648/j.ajtas.20251406.12},
  url = {https://doi.org/10.11648/j.ajtas.20251406.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20251406.12},
  abstract = {This study focuses on the recursive nonparametric estimation of the intensity function associated with a nonhomogeneous Poisson process. Accurately estimating the intensity function is crucial for understanding the dynamics of events in fields such as finance, neuroscience, and environmental monitoring. While traditional nonparametric estimators are theoretically robust, their reliance on the entire dataset for every update makes them impractical for real-time applications. To overcome this limitation, we introduce a recursive estimator that supports efficient, online updates as new data becomes available. This approach significantly lowers computational overhead while maintaining strong statistical reliability. We thoroughly analyze the asymptotic behavior of the proposed estimator, paying particular attention to the Asymptotic Mean Integrated Squared Error (AMISE), a key measure of estimation accuracy. Additionally, we compare the performance of our recursive estimator with Cucala’s non-recursive method. The results reveal that our approach achieves equivalent or superior accuracy in terms of AMISE, particularly in large-sample scenarios. A computational performance comparison further underscores the advantages of the proposed method, demonstrating its substantial reduction in execution time and its suitability for applications requiring rapid processing.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Recursive Estimation of the Intensity Function of the Non-homogeneous Poisson Process
AU  - Marcel Sihintoe Badiane
AU  - Siba Kalivogui
AU  - Bakary D Coulibaly
AU  - Aguemon Wiwegnon Uriel-Longin
Y1  - 2025/12/19
PY  - 2025
N1  - https://doi.org/10.11648/j.ajtas.20251406.12
DO  - 10.11648/j.ajtas.20251406.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 267
EP  - 276
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20251406.12
AB  - This study focuses on the recursive nonparametric estimation of the intensity function associated with a nonhomogeneous Poisson process. Accurately estimating the intensity function is crucial for understanding the dynamics of events in fields such as finance, neuroscience, and environmental monitoring. While traditional nonparametric estimators are theoretically robust, their reliance on the entire dataset for every update makes them impractical for real-time applications. To overcome this limitation, we introduce a recursive estimator that supports efficient, online updates as new data becomes available. This approach significantly lowers computational overhead while maintaining strong statistical reliability. We thoroughly analyze the asymptotic behavior of the proposed estimator, paying particular attention to the Asymptotic Mean Integrated Squared Error (AMISE), a key measure of estimation accuracy. Additionally, we compare the performance of our recursive estimator with Cucala’s non-recursive method. The results reveal that our approach achieves equivalent or superior accuracy in terms of AMISE, particularly in large-sample scenarios. A computational performance comparison further underscores the advantages of the proposed method, demonstrating its substantial reduction in execution time and its suitability for applications requiring rapid processing.

VL  - 14
IS  - 6
ER  -

Copy | Download