Georgia Institute of Technology College of Sciences

Semiparametric regressions enjoy the flexibility of nonparametric models as well as the in-terpretability of linear models. These advantages can be further leveraged with recent ad-vance in high dimensional statistics. This talk begins with a simple partially linear model,Yi = Xi β ∗ + g ∗ (Zi ) + εi , where the parameter vector of interest, β ∗ , is high dimensional butsufficiently sparse, and g ∗ is an unknown nuisance function. In spite of its simple form, this highdimensional partially linear model plays a crucial role in counterfactual studies of heterogeneoustreatment effects. In the first half of this talk, I present an inference procedure for any sub-vector (regardless of its dimension) of the high dimensional β ∗ . This method does not requirethe “beta-min” condition and also works when the vector of covariates, Zi , is high dimensional,provided that the function classes E(Xij |Zi )s and E(Yi |Zi ) belong to exhibit certain sparsityfeatures, e.g., a sparse additive decomposition structure. In the second half of this talk, I discussthe connections between semiparametric modeling and Rubin’s Causal Framework, as well asthe applications of various methods (including the one from the first half of this talk and thosefrom my other papers) in counterfactual studies that are enriched by “big data”.Abstract as a .pdf