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.
Σ Σ β β⊤Σ β⊤Σβ + σ2 ε # . Let Ik be the identity matrix inRk×k for k ∈ N. For j ∈ {0, 1}, we have Σ−1 β Σβj =
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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.