On Dantzig and Lasso estimators of the drift in a high dimensional Ornstein-Uhlenbeck model
Gabriela Ciołek, Dmytro Marushkevych, Mark Podolskij
Abstract
In this paper we present new theoretical results for the Dantzig and Lasso estimators of the drift in a high dimensional Ornstein-Uhlenbeck model under sparsity constraints. Our focus is on oracle inequalities for both estimators and error bounds with respect to several norms. In the context of the Lasso estimator our paper is strongly related to [11], where the same problem was investigated under row sparsity. We improve their rates and also prove the restricted eigenvalue property solely under ergodicity assumption on the model. Finally, we demonstrate a numerical analysis to uncover the finite sample performance of the Dantzig and Lasso estimators.
Topics & Concepts
EstimatorMathematicsLasso (programming language)ErgodicityContext (archaeology)Applied mathematicsOrnstein–Uhlenbeck processFocus (optics)Mathematical optimizationStatisticsComputer scienceStochastic processBiologyWorld Wide WebPaleontologyOpticsPhysicsStatistical Methods and InferenceStochastic processes and financial applicationsMarkov Chains and Monte Carlo Methods