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. Our approach is based on estimating \theta via an \ell_1-regularized minimization of a sample analog of L_S(\theta, ), plugging in a first-stage estimate , computed on a hold-out sample.
After revision: We develop a theory for estimation of a high-dimensional sparse parameter ), plugging in a first-stage estimate , computed on a hold-out sample.