Before revision: We propose an l1-regularized M-estimator for a high-dimensional sparse parameter that is identified by a class of semiparametric conditional moment restrictions ( CMR).
After revision: We propose an l1-regularized M-estimator for a high-dimensional sparse M-estimation by allowing the loss function to depend on a functional nuisance parameter, which we estimate by modern machine learning tools. For a class of semiparametric conditional moment restrictions ( CMR).