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Nonparametric multiple change-point estimation for analyzing large Hi-C data matrices

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  • Brault, Vincent
  • Ouadah, Sarah
  • Sansonnet, Laure
  • Lévy-Leduc, Céline

Abstract

We propose a novel nonparametric approach to estimate the location of block boundaries (change-points) of non-overlapping blocks in a random symmetric matrix which consists of random variables whose distribution changes from block to block. Our change-point location estimators are based on nonparametric homogeneity tests for matrices. We first provide some theoretical results for these tests. Then, we prove the consistency of our change-point location estimators. Some numerical experiments are also provided in order to support our claims. Finally, our approach is applied to Hi-C data which are used in molecular biology to study the influence of chromosomal conformation on cell function.

Suggested Citation

  • Brault, Vincent & Ouadah, Sarah & Sansonnet, Laure & Lévy-Leduc, Céline, 2018. "Nonparametric multiple change-point estimation for analyzing large Hi-C data matrices," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 143-165.
    • Handle: RePEc:eee:jmvana:v:165:y:2018:i:c:p:143-165
    DOI: 10.1016/j.jmva.2017.12.005
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    References listed on IDEAS

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    1. Vincent Brault & Maud Delattre & Emilie Lebarbier & Tristan Mary-Huard & Céline Lévy-Leduc, 2017. "Estimating the Number of Block Boundaries from Diagonal Blockwise Matrices Without Penalization," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 563-580, June.
    2. Haeran Cho & Piotr Fryzlewicz, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 475-507, March.
    3. Jesse R. Dixon & Siddarth Selvaraj & Feng Yue & Audrey Kim & Yan Li & Yin Shen & Ming Hu & Jun S. Liu & Bing Ren, 2012. "Topological domains in mammalian genomes identified by analysis of chromatin interactions," Nature, Nature, vol. 485(7398), pages 376-380, May.
    4. Cho, Haeran & Fryzlewicz, Piotr, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," LSE Research Online Documents on Economics 57147, London School of Economics and Political Science, LSE Library.
    5. Gabor J. Szekely & Maria L. Rizzo, 2005. "Hierarchical Clustering via Joint Between-Within Distances: Extending Ward's Minimum Variance Method," Journal of Classification, Springer;The Classification Society, vol. 22(2), pages 151-183, September.
    6. David S. Matteson & Nicholas A. James, 2014. "A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 334-345, March.
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