Power of Discrete Scan Statistics: a Finite Markov Chain Imbedding Approach

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• 作者：Wan-Chen Lee
• 关键词：FMCI ; Hypothesis test ; Power ; Scan statistics ; Primary 60E05 ; Secondary 62G10
• 刊名：Methodology and Computing in Applied Probability
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：17
• 期：3
• 页码：833-841
• 全文大小：181 KB
• 参考文献：Fu JC (2001) Distribution of the scan statistic for a sequence of bistate trials. J Appl Probab 38:908鈥?16MathSciNet View Article
  Fu JC, Johnson BC (2009) Approximate probabilities for runs and patterns in i.i.d. and Markov-dependent multistage trials. Adv Appl Probab 41:292鈥?08MathSciNet View Article
  Fu JC, Wu TL, Lou WYW (2012) Continuous, discrete and conditional scan statistics. J Appl Probab 49:199鈥?09MathSciNet View Article
  Hoh J, Ott J (2000) Scan Statistics to Scan Markers for Susceptibility Genes. Proc Natl Acad Sci U S A 97:9615鈥?617View Article
  Naus J (1974) Probabilities for a generalized birthday problem. J Am Stat Assoc 69:810鈥?15MathSciNet View Article
  Wallenstein S, Naus J, Glaz J (1994) Power of the scan statistic in detecting a changed segment in a Bernoulli sequence. Biometrika 81:595鈥?01MathSciNet View Article
  
• 作者单位：Wan-Chen Lee (1)
  
  1. University of Manitoba, Winnipeg, Canada
  
• 刊物主题：Statistics, general; Life Sciences, general; Electrical Engineering; Economics general; Business/Management Science, general;
• 出版者：Springer US
• ISSN：1573-7713

文摘

Wallenstein et al. (1994) discussed the power via combinatorial calculations for scan statistics against a pulse alternative given certain proper conditions. Our work extends their results and provides an alternative way to obtain the distribution of a scan statistic under various alternative conditions. An efficient and intuitive expression for the distribution as well as power of the scan statistic is introduced via finite Markov chain imbedding (FMCI). The numerical results of the power for a discrete scan statistic against various conditions are presented.