CAREER: New Paradigms of Estimation and Inference in Constrained Nonparametric Models

职业：约束非参数模型中估计和推理的新范式

• 批准号: 2143468
• 负责人: Qiyang Han
• 金额: $ 40万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-01 至 2027-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2143468&HistoricalAwards=false
• 关键词: CAREER; New; Paradigms; Estimation; Inference

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). Nonparametric methods are a basic toolkit for analyzing multivariate and high-dimensional data in modern statistics. However, many standard nonparametric methods are known to face two key challenges. First, the performance of these methods is usually sensitive to multiple subjective choices of tuning parameters. Second, the methods developed for the purpose of estimation typically cannot be directly used for statistical inference. This project aims to systematically develop a new paradigm of multi-dimensional nonparametric methods under natural shape constraints that simultaneously resolves these two critical issues. In particular, the shape-constrained methods to be developed in this project will not only be fully automated without ad-hoc tuning, but also enjoy simultaneous optimal estimation and inference merits. The project will integrate research with education through course development, research mentoring for undergraduate and graduate students, especially those from underrepresented groups, and summer programs. This project will focus on two complementary categories of research problems. Problems in the first category aim at understanding the potentials of a class of non-standard generalized block estimators, and the drawbacks of standard methods such as the maximum likelihood or least squares. Problems in the second category aim at developing fully automated inference procedures for several canonical local and global inference targets using the non-standard methods, in a few related models. The common ground for the solutions to these problems lies in an emerging research area of non-standard distributional characterizations of multi-dimensional shape-constrained estimators initiated recently by the PI and his coauthors.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.

该奖项是根据2021年《美国救援计划法》（公法117-2）全部或部分资助的。非参数方法是用于分析现代统计数据中多元和高维数据的基本工具包。但是，已知许多标准的非参数方法面临两个关键挑战。首先，这些方法的性能通常对调谐参数的多种主观选择敏感。其次，为估计目的而开发的方法通常不能直接用于统计推断。该项目旨在系统地开发出在自然形状约束下的多维非参数方法的新范式，同时解决这两个关键问题。特别是，本项目中要开发的形状约束方法不仅在没有临时调整的情况下完全自动化，而且还可以同时享受最佳估计和推理优点。该项目将通过课程发展，本科生和研究生的研究指导，尤其是来自代表性不足的团体的研究指导以及夏季计划。该项目将重点放在两个互补的研究问题上。第一类问题旨在了解一类非标准的广义块估计器的潜力，以及标准方法的缺点，例如最大似然或最小二乘。第二类问题旨在在一些相关模型中使用非标准方法为几个规范的本地和全局推理目标开发完全自动化的推理程序。解决这些问题解决方案的共同基础在于一个新兴的研究领域，该研究领域是由PI及其合着者最近发起的多维形状约束估计器的非标准分配特征。这项奖项反映了NSF的法定任务，并通过基金会的知识优点和广泛的影响来评估NSF的法定任务，并被认为是值得的支持。