Published

2021-01-15 — Updated on 2021-01-15

On Some Statistical Properties of the Spatio-Temporal Product Density

Sobre algunas propiedades estadísticas de la densidad producto espacio-temporal

DOI:

https://doi.org/10.15446/rce.v44n1.84779

Keywords:

Invasive meningococcal disease, Martingale theory, Ohser-type estimator, Second-order product density, Variance (en)
Enfermedad meningocócica invasiva, Teoría de martingala, Estimador de tipo Ohser, Densidad de producto de segundo orden, varianza (es)

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Authors

  • Juan F. Rodríguez Berrio University of Antioquia
  • Francisco J. Rodríguez-Cortes National University of Colombia
  • Jorge Mateu Univeristy Jaume I
  • Giada Adelfio University of Palermo

We present an extension of the non-parametric edge-corrected Ohser-type kernel estimator for the spatio-temporal product density function. We derive the mean and variance of the estimator and give a closed-form approximation for a spatio-temporal Poisson point process. Asymptotic properties of this second-order characteristic are derived, using an
approach based on martingale theory. Taking advantage of the convergence to normality, confidence surfaces under the homogeneous Poisson process are built. A simulation study is presented to compare our approximation for the variance with Monte Carlo estimated values. Finally, we apply the resulting estimator and its properties to analyse the spatio-temporal distribution of the invasive meningococcal disease in the Rhineland Regional Council in Germany.

En este artículo, presentamos un estimador para la función de densidad producto de un patrón de puntos en espacio-tiempo. Este estimador es una extensión del estimador no paramétrico de Ohser, el cuál está basado en una función Kernel y ponderado por un corrector de borde. Deducimos la media y la varianza del estimador y, a su vez, damos una aproximación analítica para el caso de un patrón Poisson (completamente aleatorio). Adicionalmente, estudiamos ciertas propiedades asintóticas de nuestro estimador utilizando un enfoque basado en la teoría de martingalas y construimos superficies de confianza para el caso de aleatoriedad completa.
Presentamos un estudio de simulación para comparar nuestra aproximación de la varianza con los valores estimados a través del método Monte Carlo. Finalmente, utilizamos nuestro estimador para
analizar la distribución espacio-temporal de los registros de una enfermedad meningocócica
invasiva en la provincia del Rin en Alemania.

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How to Cite

APA

Rodríguez Berrio, J. F., Rodríguez-Cortes, F. J., Mateu, J. and Adelfio, G. (2021). On Some Statistical Properties of the Spatio-Temporal Product Density. Revista Colombiana de Estadística, 44(1), 23–42. https://doi.org/10.15446/rce.v44n1.84779

ACM

[1]
Rodríguez Berrio, J.F., Rodríguez-Cortes, F.J., Mateu, J. and Adelfio, G. 2021. On Some Statistical Properties of the Spatio-Temporal Product Density. Revista Colombiana de Estadística. 44, 1 (Jan. 2021), 23–42. DOI:https://doi.org/10.15446/rce.v44n1.84779.

ACS

(1)
Rodríguez Berrio, J. F.; Rodríguez-Cortes, F. J.; Mateu, J.; Adelfio, G. On Some Statistical Properties of the Spatio-Temporal Product Density. Rev. colomb. estad. 2021, 44, 23-42.

ABNT

RODRÍGUEZ BERRIO, J. F.; RODRÍGUEZ-CORTES, F. J.; MATEU, J.; ADELFIO, G. On Some Statistical Properties of the Spatio-Temporal Product Density. Revista Colombiana de Estadística, [S. l.], v. 44, n. 1, p. 23–42, 2021. DOI: 10.15446/rce.v44n1.84779. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/84779. Acesso em: 28 mar. 2025.

Chicago

Rodríguez Berrio, Juan F., Francisco J. Rodríguez-Cortes, Jorge Mateu, and Giada Adelfio. 2021. “ On Some Statistical Properties of the Spatio-Temporal Product Density”. Revista Colombiana De Estadística 44 (1):23-42. https://doi.org/10.15446/rce.v44n1.84779.

Harvard

Rodríguez Berrio, J. F., Rodríguez-Cortes, F. J., Mateu, J. and Adelfio, G. (2021) “ On Some Statistical Properties of the Spatio-Temporal Product Density”, Revista Colombiana de Estadística, 44(1), pp. 23–42. doi: 10.15446/rce.v44n1.84779.

IEEE

[1]
J. F. Rodríguez Berrio, F. J. Rodríguez-Cortes, J. Mateu, and G. Adelfio, “ On Some Statistical Properties of the Spatio-Temporal Product Density”, Rev. colomb. estad., vol. 44, no. 1, pp. 23–42, Jan. 2021.

MLA

Rodríguez Berrio, J. F., F. J. Rodríguez-Cortes, J. Mateu, and G. Adelfio. “ On Some Statistical Properties of the Spatio-Temporal Product Density”. Revista Colombiana de Estadística, vol. 44, no. 1, Jan. 2021, pp. 23-42, doi:10.15446/rce.v44n1.84779.

Turabian

Rodríguez Berrio, Juan F., Francisco J. Rodríguez-Cortes, Jorge Mateu, and Giada Adelfio. “ On Some Statistical Properties of the Spatio-Temporal Product Density”. Revista Colombiana de Estadística 44, no. 1 (January 15, 2021): 23–42. Accessed March 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/84779.

Vancouver

1.
Rodríguez Berrio JF, Rodríguez-Cortes FJ, Mateu J, Adelfio G. On Some Statistical Properties of the Spatio-Temporal Product Density. Rev. colomb. estad. [Internet]. 2021 Jan. 15 [cited 2025 Mar. 28];44(1):23-42. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/84779

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