Novel Inference Procedures for Non-Standard High-Dimensional Regression Models

非标准高维回归模型的新颖推理程序

• 批准号: 2015120
• 负责人: Hui Zou
• 金额: $ 15万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-07-01 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2015120&HistoricalAwards=false
• 关键词: Novel; Inference; Procedures; Non; Standard

Statistical theory of hypothesis testing plays a fundamental role in virtually all scientific studies. In the era of big data, high-dimensional data are ubiquitous in many scientific fields such as natural sciences, social sciences, medicine, and public health. Therefore, modern applications often involve hypothesis testing under high dimensions, which calls for new statistical inference theory. As regression is the most popular statistical analysis tool in applications, some recent work has been focused on hypothesis testing in high dimensional least squares regression. However, it is well-known that the standard least squares regression model has severe limitations in real applications. This research aims to develop new statistical inference theory for more flexible high dimensional regression models. This research focuses on the development of inference theory for several important non-standard regression models under ultra-high dimensions. Specifically, the PI will develop tests for testing linear hypotheses under three models: high dimensional expectile regression, high dimensional heteroscedastic regression, and robust high dimensional regression. Asymptotic distributions of the test statistics will be established rigorously. The theoretical study will fill important gaps in the high-dimensional statistics literature. A unified efficient algorithm will be developed to tackle the computational challenges. The research will provide principled tools for studying expectile functions, for examining the heterogeneity in high dimensional data and for performing robust inference. Research training opportunities for graduate students will be provided.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.

假设检验的统计理论在几乎所有的科学研究中都起着基础作用。在大数据时代，高维数据在自然科学、社会科学、医学、公共卫生等诸多科学领域无处不在。因此，现代应用往往涉及高维下的假设检验，这就需要新的统计推断理论。由于回归是应用最广泛的统计分析工具，近年来一些研究工作集中在高维最小二乘回归的假设检验上。然而，众所周知，标准最小二乘回归模型在实际应用中有严重的局限性。本研究旨在为更灵活的高维回归模型发展新的统计推理理论。本文主要研究了几种重要的超高维非标准回归模型的推理理论的发展。具体而言，PI将在三种模型下开发测试线性假设的测试：高维期望回归，高维异方差回归和稳健高维回归。检验统计量的渐近分布将被严格地建立。理论研究将填补高维统计文献的重要空白。将开发一个统一的高效算法来解决计算方面的挑战。该研究将为研究期望函数、检查高维数据的异质性和执行稳健推理提供原则性工具。为研究生提供科研训练机会。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Exactly Uncorrelated Sparse Principal Component Analysis

完全不相关的稀疏主成分分析

• DOI: 10.1080/10618600.2023.2232843
• 发表时间: 2023
• 期刊: Journal of Computational and Graphical Statistics
• 影响因子: 2.4
• 作者: Kwon, Oh-Ran;Lu, Zhaosong;Zou, Hui
• 通讯作者: Zou, Hui

Expectile regression via deep residual networks

• DOI: 10.1002/sta4.315
• 发表时间: 2020-09
• 期刊: Stat
• 影响因子: 1.7
• 作者: Yiyi Yin;H. Zou

Fast and Exact Leave-One-Out Analysis of Large-Margin Classifiers

大余量分类器的快速准确留一分析

• DOI: 10.1080/00401706.2021.1967199
• 发表时间: 2022
• 期刊: Technometrics
• 影响因子: 2.5
• 作者: Wang, Boxiang;Zou, Hui
• 通讯作者: Zou, Hui

Coordinatewise Gaussianization: Theories and Applications

坐标高斯化：理论与应用

• DOI: 10.1080/01621459.2022.2044825
• 发表时间: 2022-02
• 期刊: Journal of the American Statistical Association
• 影响因子: 3.7
• 作者: Qing Mai;Di He;Hui Zou
• 通讯作者: Hui Zou

A Simple Method for Estimating Gaussian Graphical Models

一种估计高斯图模型的简单方法

• DOI: 10.5705/ss.202021.0273
• 发表时间: 2024
• 期刊: Statistica Sinica
• 影响因子: 1.4
• 作者: Yin, Yiyi;Song, Yang;Zou, Hui
• 通讯作者: Zou, Hui