Ir al contenido

Documat


Stein’s method, Palm theory and Poisson process approximation

  • Louis H. Y. Chen [1] ; Aihua Xia [2]
    1. [1] National University of Singapore

      National University of Singapore

      Singapur

    2. [2] University of Melbourne

      University of Melbourne

      Australia

  • Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 32, Nº. 3, 2, 2004, págs. 2545-2569
  • Idioma: inglés
  • DOI: 10.1214/009117904000000027
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • The framework of Stein’s method for Poisson process approximation is presented from the point of view of Palm theory, which is used to construct Stein identities and define local dependence. A general result (Theorem 2.3) in Poisson process approximation is proved by taking the local approach. It is obtained without reference to any particular metric, thereby allowing wider applicability. A Wasserstein pseudometric is introduced for measuring the accuracy of point process approximation. The pseudometric provides a generalization of many metrics used so far, including the total variation distance for random variables and the Wasserstein metric for processes as in Barbour and Brown [Stochastic Process. Appl. 43 (1992) 9–31]. Also, through the pseudometric, approximation for certain point processes on a given carrier space is carried out by lifting it to one on a larger space, extending an idea of Arratia, Goldstein and Gordon [Statist. Sci. 5 (1990) 403–434]. The error bound in the general result is similar in form to that for Poisson approximation. As it yields the Stein factor 1/λ as in Poisson approximation, it provides good approximation, particularly in cases where λ is large. The general result is applied to a number of problems including Poisson process modeling of rare words in a DNA sequence.


Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno