Methodology for Qualitative Constraints in Semi-Parametric Models

半参数模型中的定性约束方法

• 批准号: 2210662
• 负责人: Arun Kuchibhotla
• 金额: $ 20万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-09-01 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2210662&HistoricalAwards=false
• 关键词: Methodology; Qualitative; Constraints; Semi; Parametric

Qualitative constraints such as concavity (law of diminishing returns) are ubiquitous in social sciences and economics. In order to incorporate these important constraints into statistical modeling, users often resort to simpler models, for example, linear regression. However, these simpler models are inflexible and cannot fully explain complex scientific phenomena. In turn, semi-parametric models provide necessary flexibility and interpretability. However, in fitting these semi-parametric models, qualitative constraints are often left unexploited. Ignoring these constraints, will not only lead to a loss in interpretability but also forgo some accuracy in the performance of the estimates. The broad goal of this proposal is to develop new statistical methods that respect subject matter qualitative constraints and make such methods more accessible to researchers via open-source software implementation.This project has three main aims: (1) to develop general non-parametric regression estimators that account for available subject matter constraints and adapt to the smoothness of the underlying truth; (2) to explore systematic approaches for semi-parametric estimators that incorporate naturally occurring shape constraints on the nuisance components; and (3) to assess improved doubly robust estimators of functionals that can be represented in terms of variationally dependent nuisance parameters, whose relationship is shape-constrained on a subject matter basis. This in return would allow for significant improvement of estimation accuracy, thereby outperforming the existing tools that do not incorporate such information. The results of the project will find utility in addressing the interpretability and reproducibility concerns that have recently emerged in a broad range of domain knowledge disciplines, from social sciences to economics to epidemiology. The project will offer a multitude of opportunities for research training and professional development of the next generation of statisticians and will also engage in bolstering diversity in statistical sciences.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.

诸如凹的定性约束（回报率降低）在社会科学和经济学中无处不在。为了将这些重要约束结合到统计建模中，用户通常会诉诸更简单的模型，例如线性回归。但是，这些简单的模型不灵活，无法完全解释复杂的科学现象。反过来，半参数模型提供了必要的灵活性和解释性。但是，在拟合这些半参数模型时，定性约束通常无法解释。忽略这些限制，不仅会导致可解释性损失，而且还会放弃估计性的精确度。该提案的广泛目标是开发新的统计方法，这些方法尊重主题的定性约束，并通过开源软件实施使研究人员更容易访问此类方法。该项目具有三个主要目的：（1）开发一般的非参数回归估算值，以说明一般的非参数估算值，以说明可用的主题约束并适应下层真实的平稳性； （2）探索半参数估计器的系统方法，这些估计量包含在滋扰组件上的天然形状约束； （3）评估可以用变异依赖的滋扰参数来表示功能的双重稳健估计器，其关系在主题基础上被形状约束。作为回报，这将使估计准确性显着提高，从而优于不包含此类信息的现有工具。该项目的结果将找到解决方案，以解决最近在从社会科学到经济学到流行病学的广泛领域知识学科中出现的可解释性和可重复性问题。该项目将为下一代统计学家的研究培训和专业发展提供多种机会，还将参与统计科学领域的多样性。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审查标准通过评估来进行评估的。