High Dimensional Semiparametric Estimation and Inferences

半参数回归模型为数据科学家提供了一种分析复杂结构数据集的有用方法。它允许研究人员以线性方式对某些特征进行建模，而不会限制其余协变量的影响。这种灵活性可以大大提高预测性能，特别是当参数模型假设无效时。在实践中，半参数模型在生物统计学、计量经济学和神经科学的许多高维应用中被证明是有用的。然而，在文献中，缺乏对高维半参数模型的估计和推断的统计研究。本计画旨在为高维半参数分析奠定坚实的理论基础。这一研究将极大地促进高维复杂数据半参数分析的应用。该项目包括三个研究部分。首先，建立了高维半参数模型的频率估计理论，并对估计量的渐近性态有了新的理论认识。其次，研究人员将开发新的方法来进行高维半参数推断，如置信区间和探索相关的半参数效率问题。第三，贝叶斯对应的估计和推理理论将发展。研究者将建立贝叶斯点估计和区间估计的频率有效性。这些研究成果将为高维半参数建模提供重要的理论指导。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.