Inference in Additively Separable Models With a High Dimensional Conditioning Set

This paper considers estimation and inference of nonparametric conditional expectation relations with a high dimensional conditioning set. Rates of convergence and asymptotic normality are derived for series estimators for models where conditioning information enters in an additively separable manner and satisfies sparsity assumptions. Conditioning information is selected through a model selection procedure which chooses relevant variables in a manner that generalizes the post-double selection procedure proposed in (Belloni et al., 2014) to the nonparametric setting. The proposed method formalizes considerations for trading off estimation precision with omitted variables bias in a nonparametric setting. The results account for both flexibility in allowing an unknown functional form for the response of the outcome to regressor of interest and allow a high dimensional set of confounders. Simulation results demonstrate that the proposed estimator performs favorably in terms of size of tests and risk properties relative to other estimation strategies.