Before revision: Many objects of interest can be expressed as an L2 continuous functional of a regression, including average treatment effects, economic average consumer surplus, expected conditional covariances, and discrete choice parameters that depend on expectations. Debiased machine learning (DML) of these objects requires a learninga Riesz representer (RR). We provide here Lasso and Dantzig learners of the RR and corresponding learners of affine and other nonlinear functionals.
After revision: Many objects of interest can be expressed as an L2 continuous functional of a regression, including average treatment effects, policy effects, average derivatives, regression decompositions, economic average equivalent variation, and parameters of economic structural models. The regressions may be high dimensional. Plugging machine learners into identifying equations can lead to poor inference due to bias and/or model selection. This paper gives automatic debiasing for estimating equations and valid asymptotic inference for the estimators of effects of interest. The debiasing is automatic in that its construction uses the identifying equations without the full form of the bias correction and is performed by machine learning. Novel results include convergence rates for Lasso and Dantzig learners of the RR and corresponding learners of affine and other nonlinear functionals.