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). We estimate the nonparametric nuisance parameter by modern machine learning methods. Plugging the first-stage estimate into the CMR, we construct the M-estimator loss functionfor the target parameter so that its gradient is insensitive (formally, Neyman-orthogonal) with respect to the first-stage regularization bias.
After 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 ( CMRs), we explicitly derive the loss function. We first adjust the moment function so that the gradient of the future M-estimator loss is insensitive (formally, Neyman-orthogonal) with respect to the first-stage regularization bias.