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Estimation of high-dimensional change-points under a group sparsity structure

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  • Cai, Hanqing
  • Wang, Tengyao

Abstract

Change-points are a routine feature of ‘big data’ observed in the form of high-dimensional data streams. In many such data streams, the component series possess group structures and it is natural to assume that changes only occur in a small number of all groups. We propose a new change point procedure, called groupInspect, that exploits the group sparsity structure to estimate a projection direction so as to aggregate information across the component series to successfully estimate the change-point in the mean structure of the series. We prove that the estimated projection direction is minimax optimal, up to logarithmic factors, when all group sizes are of comparable order. Moreover, our theory provide strong guarantees on the rate of convergence of the change-point location estimator. Numer-ical studies demonstrates the competitive performance of groupInspect in a wide range of settings and a real data example confirms the practical usefulness of our procedure.

Suggested Citation

  • Cai, Hanqing & Wang, Tengyao, 2023. "Estimation of high-dimensional change-points under a group sparsity structure," LSE Research Online Documents on Economics 118366, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:118366
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    File URL: http://eprints.lse.ac.uk/118366/
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    References listed on IDEAS

    as
    1. Marguerite Frank & Philip Wolfe, 1956. "An algorithm for quadratic programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 95-110, March.
    2. Rafal Baranowski & Yining Chen & Piotr Fryzlewicz, 2019. "Narrowest‐over‐threshold detection of multiple change points and change‐point‐like features," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(3), pages 649-672, July.
    3. Tengyao Wang & Richard J. Samworth, 2018. "High dimensional change point estimation via sparse projection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(1), pages 57-83, January.
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    More about this item

    Keywords

    change-point analysis; high-dimensional data; group sparsity; EP/T02772X/1;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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