The Annals of Applied Probability

Boundary Crossing Probabilities for Locally Poisson Processes

Clive R. Loader

Full-text: Open access

Abstract

We derive large deviation approximations to boundary crossing probabilities for a class of point processes which can be approximated locally as Poisson processes. In the special case of empirical processes, we are able to obtain second order correction terms. The methods are applied to Kolmogorov-Smirnov testing, where we are able to obtain accurate approximations to the significance level when the null hypothesis is an exponential family with unknown nuisance parameters.

Article information

Source
Ann. Appl. Probab., Volume 2, Number 1 (1992), 199-228.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005778

Digital Object Identifier
doi:10.1214/aoap/1177005778

Mathematical Reviews number (MathSciNet)
MR1143400

Zentralblatt MATH identifier
0747.60047

JSTOR
links.jstor.org

Subjects
Primary: 60G55: Point processes
Secondary: 60F10: Large deviations 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Boundary crossing empirical process change point Kolmogorov-Smirnov test point process Poisson process

Citation

Loader, Clive R. Boundary Crossing Probabilities for Locally Poisson Processes. Ann. Appl. Probab. 2 (1992), no. 1, 199--228. doi:10.1214/aoap/1177005778. https://projecteuclid.org/euclid.aoap/1177005778


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