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.

该奖项全部或部分根据2021年美国救援计划法案（公法117-2）资助。非参数方法是现代统计学中分析多元和高维数据的基本工具。然而，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个主观选择敏感。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一种新的自然形状约束下的多维非参数方法，同时解决这两个关键问题。特别是，在这个项目中开发的形状约束的方法将不仅是完全自动化的，没有ad-hoc调整，但也享有同时最佳的估计和推理的优点。该项目将通过课程开发，本科生和研究生的研究指导，特别是那些来自代表性不足的群体和暑期课程，将研究与教育结合起来。该项目将侧重于两个互补的研究问题类别。第一类问题旨在了解一类非标准广义块估计的潜力，以及标准方法如最大似然法或最小二乘法的缺点。第二类问题的目的是在几个相关的模型中，使用非标准方法，为几个典型的局部和全局推理目标开发全自动推理程序。这些问题的解决方案的共同点在于一个新兴的研究领域的非标准分布特征的多维形状约束估计最近发起的PI和他的coauthors.This奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。