Sparsity of regression parameters or differential parameters is not necessary for consistent multiple change point detection in high-dimensional linear regression; a covariance discrepancy scan is statistically and computationally more efficient.
(C.29) Similarly, withψ ≍ ΞΨ log(p∆)/σ, we can show (wE t )4E max i∈[p] |ξit|4I{maxi∈[p] |ξit|>ψ} DE, QE n,p ≲ (ΞΨj)4 log3(p∆) p∆σ4
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Detection and inference of changes in high-dimensional linear regression with non-sparse structures
Sparsity of regression parameters or differential parameters is not necessary for consistent multiple change point detection in high-dimensional linear regression; a covariance discrepancy scan is statistically and computationally more efficient.