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

Hanqing Cai and Tengyao Wang

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: change-point analysis; high-dimensional data; group sparsity (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 37 pages
Date: 2023-03-03
New Economics Papers: this item is included in nep-ecm and nep-ets
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Published in Electronic Journal of Statistics, 3, March, 2023, 17(1), pp. 858 – 894. ISSN: 1935-7524

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