Targeted undersmoothing

This paper proposes a post-model selection inference procedure, called targeted undersmoothing, designed to construct uniformly valid confidence sets for functionals of sparse high-dimensional models, including dense functionals that may depend on many or all elements of the high-dimensional parameter vector. The confidence sets are based on an initially selected model and two additional models which enlarge the initial model. By varying the enlargements of the initial model, one can also conduct sensitivity analysis of the strength of empirical conclusions to model selection mistakes in the initial model. We apply the procedure in two empirical examples: estimating heterogeneous treatment effects in a job training program and estimating profitability from an estimated mailing strategy in a marketing campaign. We also illustrate the procedure's performance through simulation experiments.