Before revision: We develop a theory for estimation of a high-dimensional sparse parameter \theta defined as a minimizer of a population loss function L_D(\theta,g_0)which, in addition to \theta, depends on a, potentially infinite dimensional, nuisance parameter g_0.
After revision: We propose an l1-regularized M-estimator for a high-dimensional sparse parameter \theta defined as a minimizer of a population loss function L_D(\theta,g_0)which, in addition to \theta, depends on a, potentially infinite dimensional, nuisance parameter g_0.