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February, 1992 Boundary Crossing Probabilities for Locally Poisson Processes
Clive R. Loader
Ann. Appl. Probab. 2(1): 199-228 (February, 1992). DOI: 10.1214/aoap/1177005778


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.


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Clive R. Loader. "Boundary Crossing Probabilities for Locally Poisson Processes." Ann. Appl. Probab. 2 (1) 199 - 228, February, 1992.


Published: February, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0747.60047
MathSciNet: MR1143400
Digital Object Identifier: 10.1214/aoap/1177005778

Primary: 60G55
Secondary: 60F10 , 60G40

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

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.2 • No. 1 • February, 1992
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