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False Discovery Control for Scan Clustering

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Scan Statistics

Part of the book series: Statistics for Industry and Technology ((SIT))

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Abstract

This chapter describes and summarizes methods for identifying the presence of clusters in a random field. The approach is based on controlling the fraction of false discoveries and considers a density estimator as the test statistic. A procedure called shaving is adopted for correcting the bias of the density estimator. This type of scanning for cluster identification does not use a window of fixed size; the role of the window size is played by the bandwidth of the kernel estimator. Clusters obtained using different bandwidths are combined in order to increase the detection power of the procedure. In this chapter we stress some more intuitive aspects of these procedures and present some applications.

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References

  1. Adler, R.J. (2000). On excursion sets, tube formulas and maxima of random fields. The Annals of Applied Probability, 10, 1–74.

    MATH  MathSciNet  Google Scholar 

  2. Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, Series B, 57, 289–300.

    MATH  MathSciNet  Google Scholar 

  3. Chaudhuri, P. and Marron, J.S. (2000). Scale space view of curve estimation. The Annals of Statistics, 28, 408–428.

    Article  MATH  MathSciNet  Google Scholar 

  4. Genovese, C. and Wasserman, L. (2004). A stochastic process approach to false discovery control. The Annals of Statistics, 32, 1035–1061.

    Article  MATH  MathSciNet  Google Scholar 

  5. Glaz, J., Naus, J. and Wallenstein, S. (2001). Scan Statistics, Springer, New York.

    MATH  Google Scholar 

  6. Patil, G.P. and Taillie, C. (2003). Geographic and network surveillance via scan statistics for critical area detection. Statistical Science, 18, 457–465.

    Article  MATH  MathSciNet  Google Scholar 

  7. Perone-Pacifico, M., Genovese, C., Verdinelli, I. and Wasserman, L. (2004). False discovery control for random fields. Journal of the American Statistical Association, 99, 1002–1014.

    Article  MathSciNet  Google Scholar 

  8. Perone-Pacifico, M., Genovese, C., Verdinelli, I. and Wasserman, L. (2007). Scan clustering: a false discovery approach. Journal of Multivariate Analysis, 98, 1441–

    Google Scholar 

  9. Piterbarg, V.I. (1996). Asymptotic Methods in the Theory of Gaussian Processes and Fields, American Mathematical Society. Providence, RI.

    MATH  Google Scholar 

  10. van der Laan, M., Dudoit, S. and Pollard, K. (2006). Augmentation procedures for control of the generalized family-wise error rate and tail probabilities for the proportion of false positives. Statistical Applications in Genetics and Molecular Biology, 3.

    Google Scholar 

  11. Worsley, K.J. (1994). Local maxima and the expected Euler characteristic of excursion sets of χ2, F and t fields. Advances in Applied Probability, 26, 13–42.

    Article  MATH  MathSciNet  Google Scholar 

  12. Worsley, K.J. (1995). Estimating the number of peaks in a random field using the Hadwiger characteristic of excursion sets, with applications to medical images. The Annals of Statistics, 23, 640–669.

    Article  MATH  MathSciNet  Google Scholar 

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© 2009 Birkhäuser Boston, a part of Springer Science+Business Media, LLC

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Perone-Pacifico, M., Verdinelli, I. (2009). False Discovery Control for Scan Clustering. In: Glaz, J., Pozdnyakov, V., Wallenstein, S. (eds) Scan Statistics. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4749-0_13

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