Abstract:We study drift estimation for discretely observed high-dimensional Lévy-driven Ornstein--Uhlenbeck processes when the drift admits a low-rank-plus-sparse approximation. A localized, increment-truncated pseudo-likelihood is regularized by nuclear and entrywise $\ell_1$ norms. A weighted joint-cone argument and restricted cancellation condition yield non-asymptotic Frobenius oracle inequalities for exact and approximate structure. The stochastic complexity is $rd+s\log d$, with explicit discretization, truncation, and Lévy-regime sample-complexity terms. We derive operator- and infinity-norm score bounds from a Gaussian-width inequality and give a proximal-gradient algorithm. In 100-replicate experiments with mixed low-rank-plus-sparse drift, the estimator reduces mean relative Frobenius error by 4.4--5.9\% versus localized Lasso and wins 89--92\% of paired paths. Component diagnostics show that these gains concern recovery of the total drift rather than exact identification of its low-rank and sparse components.
From: Marina Palaisti Prof Dr [view email]
[v1]
Thu, 12 Mar 2026 15:26:35 UTC (12 KB)
[v2]
Mon, 23 Mar 2026 22:28:41 UTC (14 KB)
[v3]
Mon, 31 Aug 2026 20:20:12 UTC (17 KB)
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