The Annals of Statistics

A Log-Linear Model for a Poisson Process Change Point

Clive R. Loader

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Abstract

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

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

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348774

Digital Object Identifier
doi:10.1214/aos/1176348774

Mathematical Reviews number (MathSciNet)
MR1186255

Zentralblatt MATH identifier
0781.62136

JSTOR
links.jstor.org

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1176348774


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