Hybrid Methods for Statistical and Econometric Modeling

该研究项目将开发统计方法，以解释大多数模型只代表近似现实的不可避免的事实，研究人员经常面临着许多不同的合理模型的选择。该项目将从沿着三个方面解决这一问题：（i）通过设计对经济学和统计学中广泛使用的矩法方法的修改，这些方法解释了不完全测量的数据，（ii）通过提供正式的统计方法，解释了研究人员通常根据他们拥有的数据量调整其模型的复杂性的事实，以及（iii）开发预测方法，将多个（可能不完美的）模型的预测结合起来，以产生更可靠的预测。为了实现这一目标，在非常不同的研究领域开发的技术将被结合和增强，它们在与最初设想的环境非常不同的环境中的优势将得到利用。所开发的方法通常可以应用于采用统计建模的许多研究领域，从而可能影响医学、天气预报、流行病演变预测、气候建模或社会干预计划有效性评估等不同领域。研究生将参与研究过程，并公开实现新方法的计算机程序。该研究项目将解决当数据拒绝模型时为矩量法分配逻辑解释的问题。这个问题将通过确定在数据和模型之间达成一致所需的最小测量误差量来解决。这一方法将借鉴两个目前非常活跃的研究领域，即经验可能性和最佳运输。该项目的另一部分将为研究人员提供方法，通过利用非标准推断一般领域的技术进行统计推断时，解释他们的模型选择过程。最后，该项目将利用在很大程度上被忽视的事实，即多模型预测过程可以被写为模型选择问题，其中模型选择变量可以被设定值，从而强调与所谓的集合识别模型的联系，近年来受到了相当大的关注。该研究将提供一个自然的频率对应常用的贝叶斯方法，多模式forecasts.This奖项反映了NSF的法定使命，并已被认为是值得的支持，通过评估使用基金会的知识价值和更广泛的影响审查标准。

This research project will develop statistical methods that account for the unavoidable fact that most models only represent approximations to reality, and researchers often are faced with a choice of a number of different plausible models. The project will tackle this issue along three fronts: (i) by devising a modification to the widely used method-of-moment approaches from economics and statistics that account for imperfectly measured data, (ii) by providing formal statistical methods that account for the fact that researchers typically adapt the complexity of their model based on the amount of data they have, and (iii) by developing forecasting methods that combine the predictions of multiple (possibly imperfect) models to yield more robust forecasts. To accomplish this, techniques developed in very diverse fields of study will be combined and augmented, and their advantages in contexts very different from where they initially were conceived will be leveraged. The methods to be developed generally can be applied in many areas of study that employ statistical modeling and thus could impact fields as diverse as medicine, weather forecasting, pandemic evolution predictions, climate modeling, or the evaluation of the effectiveness of social intervention programs. Graduate students will be involved in the research process, and computer programs implementing the new methods will be made publicly available.This research project will solve the problem of assigning a logical interpretation to the method of moments when the data rejects the model. The problem will be addressed by determining the minimum amount of measurement error that would be needed to reach agreement between the data and the model. This approach will draw from two currently very active areas of research, namely, empirical likelihood and optimal transport. Another part of the project will provide researchers with methods to account for their model selection process when making statistical inference by leveraging techniques from the general field of nonstandard inference. Finally, the project will exploit the largely overlooked fact that a multi-model forecasting process can be written as a model selection problem, where the model selection variables can be set-valued, thus emphasizing a connection with the so-called set-identified models, which have received considerable attention in recent years. The research will provide a natural frequentist counterpart to the commonly used Bayesian approaches to multi-model forecasts.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.