Methodology for Qualitative Constraints in Semi-Parametric Models

诸如收益递减律（law of diminishing returns）之类的定性约束在社会科学和经济学中无处不在。为了将这些重要的约束纳入统计建模，用户通常采用更简单的模型，例如线性回归。然而，这些简单的模型是不灵活的，不能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可解释性。然而，在拟合这些半参数模型时，定性约束往往未被利用。忽略这些约束，不仅会导致可解释性的损失，而且还会放弃估计性能的某些准确性。该项目的主要目标是开发新的统计方法，尊重主题的定性约束，并使这些方法更容易通过开源软件实现的研究人员。该项目有三个主要目标：（1）开发通用的非参数回归估计，占现有的主题约束，并适应平滑的基本真理;（2）探索半参数估计的系统方法，将自然发生的形状约束的滋扰组件;和（3）评估改进的双重鲁棒估计的泛函，可以表示在变分相关的滋扰参数，其关系是形状约束的主题的基础上。反过来，这将大大提高估计的准确性，从而优于没有纳入此类信息的现有工具。该项目的结果将在解决可解释性和再现性问题中找到实用性，这些问题最近出现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。该项目将为下一代统计学家的研究培训和专业发展提供大量机会，并将参与支持统计科学的多样性。该奖项反映了NSF的法定使命，并被认为值得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来支持。

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.