TITLE: High Dimensional Inference: Semiparametrics, Counterfactuals, and Heterogeneity
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 advance in high dimensional statistics. This talk begins with a simple partially linear model, Yi = Xiβ∗ + g∗(Zi) + εi, where the parameter vector of interest, β∗, 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 β∗. This method does not require the “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 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 (in- cluding the one presented in this talk and those from my other papers) in counterfactual studies that are enriched by “big data”.
BIO: Ying Zhu joined the department of Economics and Social Science Data Analytics Initiative as a research associate at Michigan State University in September 2015. She received her M.S. degree in Civil and Environmental Engineering from MIT, M.A. degree in Statistics from UC Berkeley, and PhD degree in Business Administration from Haas School of Business at UC Berkeley. During her PhD education at U.C. Berkeley, her research interest has evolved into high dimensional statistics. Built upon knowledge from econometrics, statistics, and machine learning, her past and current contribution to this field can be summarized as “methods and theory for high dimensional (causal) estimation and inference”. Many of the problems she has worked on can be potentially related to the Rubin Causal Model (RCM) framework when it is enriched by the availability of high dimensional data.