High Dimensional Semiparametric Estimation and Inferences

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Semiparametric regression model provides data scientists a useful way to analyze complex-structured data sets. It allows researchers to model some features in a linear way, without restricting the effect of the rest covariates. This flexibility can greatly enhance the prediction performance especially when parametric model assumptions are invalid. In practice, the semiparametric modelling is proven useful in many high dimensional applications in Biostatistics, Econometrics and Neuroscience. However in literature, there is a lack of statistical studies on the estimation and inference of high dimensional semiparametric model. This project aims to lay a solid theoretical foundation for high dimensional semiparametric analysis, in both frequentist and Bayesian paradigms. This research will significantly promote the use of semiparametric analysis of high dimensional complex data. This project consists of three research components. First, the investigators will establish the frequentist estimation theory and obtain new theoretical insights on the asymptotic behavior of the estimators in high dimensional semiparametric model. Secondly, the investigators will develop novel approach to conduct high dimensional semiparametric inferences such as confidence intervals and explore related semiparametric efficiency issue. Thirdly, Bayesian counterparts of estimation and inference theories will be developed. The investigators will establish the frequentist validity of Bayesian point estimations and interval estimations. These research results will provide important theoretical guidelines for high dimensional semiparametric modeling.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.