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Clustering with statistical error control

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  • Michael Vogt
  • Matthias Schmid

Abstract

This article presents a clustering approach that allows for rigorous statistical error control similar to a statistical test. We develop estimators for both the unknown number of clusters and the clusters themselves. The estimators depend on a tuning parameter α which is similar to the significance level of a statistical hypothesis test. By choosing α, one can control the probability of overestimating the true number of clusters, while the probability of underestimation is asymptotically negligible. In addition, the probability that the estimated clusters differ from the true ones is controlled. In the theoretical part of the article, formal versions of these statements on statistical error control are derived in a baseline model with convex clusters. A simulation study and two applications to temperature and gene expression microarray data complement the theoretical analysis.

Suggested Citation

  • Michael Vogt & Matthias Schmid, 2021. "Clustering with statistical error control," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 729-760, September.
  • Handle: RePEc:bla:scjsta:v:48:y:2021:i:3:p:729-760
    DOI: 10.1111/sjos.12450
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    References listed on IDEAS

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    1. Inder Tecuapetla-Gómez & Axel Munk, 2017. "Autocovariance Estimation in Regression with a Discontinuous Signal and m-Dependent Errors: A Difference-Based Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 346-368, June.
    2. Jiahua Chen & Pengfei Li & Yuejiao Fu, 2012. "Inference on the Order of a Normal Mixture," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1096-1105, September.
    3. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    4. Li, Pengfei & Chen, Jiahua, 2010. "Testing the Order of a Finite Mixture," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1084-1092.
    5. Ranjan Maitra & Volodymyr Melnykov & Soumendra N. Lahiri, 2012. "Bootstrapping for Significance of Compact Clusters in Multidimensional Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 378-392, March.
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