On Lasso and Slope drift estimators for Lévy-driven Ornstein–Uhlenbeck processes

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 min-imax optimal rate of convergence (up to numerical constants), for tuning parameters chosen independently of the confidence level, which improves the previously obtained results for standard Ornstein–Uhlenbeck processes.