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Large-deviation approximations to the distribution of scanstatistics

Published online by Cambridge University Press:  01 July 2016

Catherine Loader
Catherine Loader*
Affiliation:
AT&T Bell Laboratories
*
∗Postal address: AT&TBell Laboratories, Room 2C-279, 600 Mountain Avenue, Murray Hill, NJ 07974,USA.
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Abstract

Suppose a Poisson process is observed on the unit interval. The scan statistic isdefined as the maximum number of events observed as a window of fixed width ismoved across the interval, and the distribution under homogeneity has beenwidely studied. Frequently, we may not wish to specify the window width inadvance but to consider scan statistics with varying window widths. We propose amodification of the scan statistic based on a likelihood ratio criterion. Thisleads to a boundary-crossing problem for a two-dimensional random field, whichwe approximate using a large-deviation scaling under homogeneity. Similarresults are obtained for Poisson processes observed in two dimensions. Numericalcomputations and simulations are used to illustrate the accuracy of theapproximations.

Keywords

BOUNDARY CROSSINGCHANGE POINTSPOISSON PROCESSRANDOM FIELDSPATIAL STATISTICS
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 4 , December 1991 , pp. 751 - 771
Copyright
Copyright © Applied Probability Trust 1991 

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