Approximations for two-dimensional discrete scan statistics in some block-factor type dependent models

Amarioarei, Alexandru; Preda, Cristian

doi:10.1016/j.jspi.2014.05.002

Cited by 8 publications

(4 citation statements)

References 18 publications

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“…, S 3m 1 ,3m 2 ,3m 3 . In order to obtain reasonable simulation errors for these quantities, as in Amarioarei and Preda (2014), the authors use the importance sampling method introduced in Naiman and Priebe (2001).…”

Section: Three Dimensional Discrete Scan Statisticsmentioning

confidence: 99%

Scan Statistics Viewed as Maximum of 1-Dependent Random Variables

Haiman¹,

Preda

2018

Handbook of Scan Statistics

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Section: Three Dimensional Discrete Scan Statisticsmentioning

confidence: 99%

Scan Statistics Viewed as Maximum of 1-Dependent Random Variables

Haiman¹,

Preda

2018

Handbook of Scan Statistics

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“…Obviously, it is not applicable here. Luckily, there are different ways to give the accurate approximation for P(S ≥ k) and one of them is using the Haiman theorem [18][19][20].…”

Section: Approximation For P(s ≥ K)mentioning

confidence: 99%

Scan statistics with local vote for target detection in distributed system

Luo

2017

EURASIP J. Adv. Signal Process.

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Target detection has occupied a pivotal position in distributed system. Scan statistics, as one of the most efficient detection methods, has been applied to a variety of anomaly detection problems and significantly improves the probability of detection. However, scan statistics cannot achieve the expected performance when the noise intensity is strong, or the signal emitted by the target is weak. The local vote algorithm can also achieve higher target detection rate. After the local vote, the counting rule is always adopted for decision fusion. The counting rule does not use the information about the contiguity of sensors but takes all sensors' data into consideration, which makes the result undesirable. In this paper, we propose a scan statistics with local vote (SSLV) method. This method combines scan statistics with local vote decision. Before scan statistics, each sensor executes local vote decision according to the data of its neighbors and its own. By combining the advantages of both, our method can obtain higher detection rate in low signal-to-noise ratio environment than the scan statistics. After the local vote decision, the distribution of sensors which have detected the target becomes more intensive. To make full use of local vote decision, we introduce a variable-step-parameter for the SSLV. It significantly shortens the scan period especially when the target is absent. Analysis and simulations are presented to demonstrate the performance of our method.

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“…We have used N = 1,000, 000 trials for all simulations to evaluate the two approximations and the error bound. One may also refer to Amȃrioarei and Preda (2014) for more discussion about efficient estimation of approximation 2 and the error bound. From the numerical results presented in Tables 1 -2, it is evident that the two approximations performed well.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

“…Since then scan statistics for two dimensional data have been of great interest in the scientific literature, due to important applications in many areas of science and technology, including: astronomy, biosurveillance, computer science, electrical engineering, epidemiology, food sciences, geography, health and medical sciences, material science, physics, reconnaissance and reliability of systems (Glaz 1996, Glaz and Balakrishnan 1999, Glaz et al 2001, Guerriero et al 2009, Amȃrioarei and Preda 2014and Wang and Glaz 2014. Most of the research in the area of scan statistics has been focused on detecting a local change in the mean of the observed data.…”

Section: Introductionmentioning

confidence: 99%

Scan statistics for detecting a local change in variance for two-dimensional normal data

Zhao

Glaz

2016

Communications in Statistics - Theory and Methods

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In this article scan statistics for detecting a local change in variance for two dimensional normal data are discussed. When the precise size of the rectangular window where a local change in variance has occurred is unknown, multiple and variable window scan statistics are proposed. A simulation study is presented to evaluate the performance of the scan statistics investigated in this article via comparison of power. A method for estimating the rectangular region where a change in variance has occurred and the size of the change in variance is also discussed.

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Approximations for two-dimensional discrete scan statistics in some block-factor type dependent models

Abstract: We consider the two-dimensional discrete scan statistic generated by a block-factor type model obtained from i.i.d. sequence. We present an approximation for the distribution of the scan statistics and the corresponding error bounds. A simulation study illustrates our methodology.

Cited by 8 publications

References 18 publications

Scan Statistics Viewed as Maximum of 1-Dependent Random Variables

Scan Statistics Viewed as Maximum of 1-Dependent Random Variables

Scan statistics with local vote for target detection in distributed system

Scan statistics for detecting a local change in variance for two-dimensional normal data

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