On Rescaled Poisson Processes and the Brownian Bridge

Author: Schoenberg F.P.

Source: Annals of the Institute of Statistical Mathematics, Volume 54, Number 2, 2002 , pp. 445-457(13)

Publisher: Springer

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Abstract:

The process obtained by rescaling a homogeneous Poisson process by the maximum likelihood estimate of its intensity is shown to have surprisingly strong self-correcting behavior. Formulas for the conditional intensity and moments of the rescaled Poisson process are derived, and its behavior is demonstrated using simulations. Relationships to the Brownian bridge are explored, and implications for point process residual analysis are discussed.

Keywords: Brownian bridge; Poisson bridge; intensity; point process; Poisson process; residual analysis

Language: English

Document Type: Research article

Affiliations: 1: Department of Statistics, University of California, Los Angeles, Los Angeles, CA 90095-1554, U.S.A., e-mail: frederic@stat.ucla.edu

Publication date: 2002-01-01