Methodology for Qualitative Constraints in Semi-Parametric Models

在社会科学和经济学中，诸如凹凸性（收益递减规律）之类的定性约束无处不在。为了将这些重要的约束合并到统计建模中，用户经常求助于更简单的模型，例如线性回归。然而，这些简单的模型缺乏灵活性，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，通常没有利用定性约束。忽略这些约束不仅会导致可解释性的损失，而且还会在评估的执行中放弃一些准确性。该提案的总体目标是开发新的统计方法，这些方法尊重主题的定性限制，并通过开源软件实现使研究人员更容易使用这些方法。该项目有三个主要目标：(1)开发一般的非参数回归估计器，该估计器考虑了可用的主题约束并适应潜在真理的平滑性；(2)探索半参数估计的系统方法，其中包括对干扰分量的自然形状约束；(3)评估改进的双鲁棒函数估计器，这些函数可以用变量相关的干扰参数表示，其关系在主题基础上受到形状约束。作为回报，这将大大提高估计的准确性，从而优于不包含此类信息的现有工具。该项目的结果将有助于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大量机会，并将促进统计科学的多样性。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。

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.