THE MAXIMUM OF A RATCHET SCANNING PROCESS OVER A POISSON RANDOM FIELD

Scan statistic is a popular method in searching non-random clusters over some random field. Motivated by a high energy particle detection problem, we are interested in a ratchet scan statistic whose scanning window is a grid set, instead of a rectangular box. We further generalize it to an r-dimensi...

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Bibliographic Details
Published in:Statistica Sinica 2013-10, Vol.23 (4), p.1541-1551
Main Author: Tu, I-Ping
Format: Article
Language:English
Subjects:
Approximation
Cosmic rays
Integers
Muons
Poisson process
Probabilities
Quantum statistics
Radiation counters
Random variables
Ratchet effect
Online Access:Get full text
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Summary:Scan statistic is a popular method in searching non-random clusters over some random field. Motivated by a high energy particle detection problem, we are interested in a ratchet scan statistic whose scanning window is a grid set, instead of a rectangular box. We further generalize it to an r-dimensional problem for any r ∈ ℤ+ and provide a tail probability approximation for a ratchet scan statistic over an r-dimensional homogeneous Poisson process. We show that the ratchet effect can be factored out as an overshoot function ν in each dimension.
ISSN:1017-0405
1996-8507
DOI:10.5705/ss.2012.062s