High Dimensional Semiparametric Estimation and Inferences

高维半参数估计和推论

基本信息

批准号：
1811812
负责人：
Qifan Song
金额：
$ 16万
依托单位：
Purdue University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-08-15 至 2021-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1811812&HistoricalAwards=false
关键词：
Dimensional Semiparametric Estimation Inferences

项目摘要

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.

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，而无需限制其余协变量的效果。这种灵活性可以大大提高预测性能，尤其是当参数模型假设无效时。实际上，半参数建模在生物统计学，计量学和神经科学中的许多高维应用中被证明是有用的。然而，在文献中，缺乏关于高维半参数模型的估计和推断的统计研究。该项目旨在在频繁主义和贝叶斯范式中为高维半参数分析奠定坚实的理论基础。这项研究将显着促进对高维复杂数据的半参数分析的使用。该项目由三个研究组成部分组成。首先，研究人员将建立频繁的估计理论，并获得有关估计量在高维半参数模型中的渐近行为的新理论见解。其次，研究人员将开发新的方法来进行高维半参数推断，例如置信区间，并探索相关的半参数效率问题。第三，将开发估计和推理理论的贝叶斯对应物。研究人员将确定贝叶斯点估计和间隔估计的频繁有效性。这些研究结果将为高维半理论建模提供重要的理论指南。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响评估标准通过评估来支持的。