The Annals of Statistics

A Log-Linear Model for a Poisson Process Change Point

Clive R. Loader

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Many methods have been proposed for modelling nonhomogeneous Poisson processes, including change point models and log-linear models. In this paper, we use likelihood ratio tests to choose which of these models are necessary. Of particular interest is the test for the presence of a change point, for which standard asymptotic theory is not valid. Large deviation methods are applied to approximate the significance level, and power approximations are given. Confidence regions for the change point and other parameters in the model are also derived. A British coal mining accident data set is used to illustrate the methodology.

Article information

Ann. Statist., Volume 20, Number 3 (1992), 1391-1411.

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62M99: None of the above, but in this section
Secondary: 60G55: Point processes 62F03: Hypothesis testing

Boundary crossing change points $\log$-linear model non-nested hypothesis Poisson process


Loader, Clive R. A Log-Linear Model for a Poisson Process Change Point. Ann. Statist. 20 (1992), no. 3, 1391--1411. doi:10.1214/aos/1176348774.

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