High Dimensional Inference: Semiparametrics, Counterfactuals, and Heterogeneity

Ying Zhu, Michigan State University

Friday, January 12, 2018 - 3:30pm
​Semiparametric regressions enjoy the flexibility of nonparametric models as well as the interpretability of linear models. These advantages can be further leveraged with recent advance in high dimensional statistics. This talk begins with a simple partially linear model, _{i}=\mathbf{X}_{i}\boldsymbol{\beta}^{*}+g^{*}(\mathbf{Z}_{i})+\varepsilon_{i}, where the parameter vector of interest, \boldsymbol{\beta}^{*}, is high dimensional but sufficiently sparse, and g^{*} is an unknown nuisance function. In spite of its simple form, this high dimensional partially linear model plays a crucial role in counterfactual studies of heterogeneous treatment effects. I present an inference procedure for any sub-vector (regardless of its dimension) of the high dimensional \boldsymbol{\beta}^{*}. This method does not require the “beta-min” condition and also works when the vector of covariates, \mathbf{Z}_{i}, is high dimensional, provided that the function classes \mathbb{E}(X_{ij}\vert\mathbf{Z}_{i})s and \mathbb{E}(Y_{i}\vert\mathbf{Z}_{i}) belong to exhibit certain sparsity features, e.g., a sparse additive decomposition structure. In this talk, I also discuss the connections between semiparametric modeling and Rubin's Causal Framework, as well as the applications of various methods (including the one presented in this talk and those from my other papers) in counterfactual studies that are enriched by “big data”.

Seminars generally take place in 116 Old Chemistry Building on Fridays from 3:30 - 4:30 pm. For additional information contact: karen.whitesell@duke.edu or phone 919-684-8029. Sorry, but we do not have reprints available. Please feel free to contact the authors by email for follow-up information, articles, etc. Reception following seminar in 211 Old Chemistry

Old Chemistry 116

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