Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/19122
Title: Scan Statistics of Rate Function of Scores on Poisson Point Processes
Authors: YU XIAOJIANG
Keywords: Change of Measure, Large Deviation, Marked Poisson Process, Scan Statistics
Issue Date: 30-Jul-2010
Source: YU XIAOJIANG (2010-07-30). Scan Statistics of Rate Function of Scores on Poisson Point Processes. ScholarBank@NUS Repository.
Abstract: Let X1,X2, ... be independent and identically distributed (i.i.d.) random variables with positive mean. Each random variable Xi is associated with a random time ti and t1, t2, ... are distributed according to a Poisson point process on [0, 1]. We would like to detect unusual behavior in a segment of the interval [0, 1]. For each 0 < x < y < 1, we compute a score S(x, y) which is large when there is unusual behavior in the interval [x, y]. Since x, y are unknown, we consider the maximum of these scores over 0 < x < y < 1, known in the statistical literature as scan statistics. We derive formulas for approximating the tail probabilities of these scan statistics and check them through numerical computations and simulation exercises.
URI: http://scholarbank.nus.edu.sg/handle/10635/19122
Appears in Collections:Master's Theses (Open)

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