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Inference in high-dimensional online changepoint detection

Author

Listed:
  • Chen, Yudong
  • Wang, Tengyao
  • Samworth, Richard J.

Abstract

We introduce and study two new inferential challenges associated with the sequential detection of change in a high-dimensional mean vector. First, we seek a confidence interval for the changepoint, and second, we estimate the set of indices of coordinates in which the mean changes. We propose an online algorithm that produces an interval with guaranteed nominal coverage, and whose length is, with high probability, of the same order as the average detection delay, up to a logarithmic factor. The corresponding support estimate enjoys control of both false negatives and false positives. Simulations confirm the effectiveness of our methodology, and we also illustrate its applicability on the U.S. excess deaths data from 2017 to 2020. The supplementary material, which contains the proofs of our theoretical results, is available online.

Suggested Citation

  • Chen, Yudong & Wang, Tengyao & Samworth, Richard J., 2023. "Inference in high-dimensional online changepoint detection," LSE Research Online Documents on Economics 119449, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:119449
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    File URL: http://eprints.lse.ac.uk/119449/
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    More about this item

    Keywords

    confidence interval; sequential method; sparsity; support estimate; EP/T02772X/1; EP/P031447/1;
    All these keywords.

    JEL classification:

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

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