Detecting sparse change in regression coefficients in the presence of dense nuisance parameters

Fengnan Gao and Tengyao Wang

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

Abstract: We introduce a new methodology ‘charcoal’ for estimating the location of sparse changes in high-dimensional linear regression coefficients, without assuming that those coefficients are individually sparse. The procedure works by constructing different sketches (projections) of the design matrix at each time point so as to eliminate the possible dense nuisance parameters. The sequence of sketched design matrices is then compared against a single sketched response vector to form a sequence of test statistics whose behavior shows a surprising link to the well-known CUSUM statistics of univariate changepoint analysis. The procedure is computationally attractive, and strong theoretical guarantees are derived for its estimation accuracy. Simulations confirm that our methods perform well in extensive settings, and a real-world application to a large single-cell RNA sequencing dataset showcases the practical relevance.

Keywords: high-dimensional regression; changepoint; nuisance parameter; sparsity (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2026-06-30
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Published in Information and Inference: A Journal of the IMA, 30, June, 2026, 15(2). ISSN: 2049-8764

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