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Variable Window Scan Statistics for Normal Data

Xiao Wang and Joseph Glaz

Communications in Statistics - Theory and Methods, 2014, vol. 43, issue 10-12, 2489-2504

Abstract: In this article, approximations and inequalities for the distribution of a two dimensional scan statistic are derived for independently and identically distributed observations from a continuous distribution. The accuracy of these approximations and inequalities is investigated for a normal model. The cases of mean and variance being known and unknown are discussed. Based on approximations for the distributions of one and two dimensional fixed window scan statistics, variable window scan statistics are introduced. We investigate the performance of these variable window scan statistics as test statistics for detection of a local change in the mean of a normal distribution. By utilizing R algorithms for the multivariate normal and t$\mathit {t}$ distributions established by Genz and Bretz (2009), numerical results are presented to evaluate the efficiency of implementing the variable window scan statistics and compare their performance, via power calculations, with fixed window scan statistics. It is evident from the numerical results that if the dimension of the window where a change has occurred is unknown, the variable window scan statistics outperform the fixed window scan statistics.

Date: 2014
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DOI: 10.1080/03610926.2013.782201

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