Appears in collection : 2022 - T3 - WS1 - Non-linear and high dimensional inference

We investigate the problem of estimating the drift parameter of a high-dimensional Lévy-driven Ornstein–Uhlenbeck process under sparsity constraints. It is shown that both Lasso and Slope estimators achieve the minimax optimal rate of convergence (up to numerical constants), for tuning parameters chosen independently of the confidence level. The results are non-asymptotic and hold both in probability and conditional expectation with respect to an event resembling the restricted eigenvalue condition. (Based on joint work with Niklas Dexheimer)