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.
Finally, by (C.8) and Lemma 7 of Wang and Samworth (2018), we have T3 ≥ 2(1 − 8C0/c′) 3 √ 6 |bθ − θ|√ ∆◦ |Σδj|∞
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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.