On Some Statistical Properties of the Spatio-Temporal Product Density

• Autores: Felipe Rodríguez-Berrio, Francisco Rodríguez Cortés, Jorge Mateu, Giada Adelfio
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 44, Nº. 1, 2021, págs. 23-41
• Idioma: inglés
• DOI: 10.15446/rce.v44n1.84779
• Títulos paralelos:
  • Sobre algunas propiedades estadísticas de la densidad producto espacio-temporal
• Enlaces
  • Texto completo
• Resumen
  • English

    Abstract 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.

  • português

    Resumen 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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