Nonparametric Inference for Convex Functions and Continuous Treatment Effects

凸函数和连续治疗效果的非参数推理

• 批准号: 2210312
• 负责人: Charles Doss
• 金额: $ 15万
• 依托单位: University of Minnesota-Twin Cities
• 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 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2210312&HistoricalAwards=false
• 关键词: Nonparametric; Inference; Convex; Functions; Continuous

It is both advantageous and necessary in the modern data landscape to use statistical methods that are very flexible and allow the data to "speak for themselves," rather than having researchers make strong unjustifiable prior assumptions about the data. Unfortunately, such flexible methods generally require the practitioner to "tune" the methods in order to get reliable results. This introduces an ad-hoc element to data analysis and, if incorrectly tuned, such statistical procedures may return incorrect results. One broad theme of this project is the development of statistical methods (relying on convexity) that are both very flexible and also fully automated, meaning they do not depend on user-chosen tuning parameters. Another theme is studying very flexible yet efficient procedures for learning about causality when the treatment variable is continuous (e.g., "what was your drug dosage," in the setting of a drug treating an illness) rather than binary ("did you receive the drug, yes or no"); it will use the fully automated methods from the first theme also in the second theme. It will focus on going beyond estimation and actually performing inference, meaning that it will quantify how reliable the estimates actually are so they can be used for policy/decision making. In the causal setting, it will consider varied examples such as the effect of number of nurse staffing hours on hospital efficacy, clinical measurements such as BMI (body mass index) on health outcomes, or time spent on education on career outcomes. The tuning parameter-free procedures based on convexity have many uses in the study of economic data and in optimization questions arising in operations research.This project is focused on several nonstandard statistical problems that are unified practically by their answering sophisticated questions in modern data settings, and are unified theoretically by their having non-standard rates of convergence and, frequently, non-normal limit distributions. The investigator will consider the following two broad thrusts: (a) nonparametric estimation and inference for shape-constrained convex functions, (b) performing nonparametric tests and/or confidence intervals for a causal continuous treatment effect curve (based on observational data) and related parameters. It is often preferable to use flexible nonparametric methods so that estimation and inference yield reliable results without depending on strong assumptions. Unfortunately, most classical nonparametric methods rely heavily on selection of (potentially many) tuning parameter(s), whose selection can be challenging. In this project, the investigator will study so-called shape constraints that are nonparametric and yet also allow estimation/inference without requiring the choice of a tuning parameter. Assessing causality is one of the most fundamental, but also challenging, tasks of scientific inquiry. With observational data, the gold standard are so-called doubly robust estimators, where “doubly robust” means optimally efficient. The investigator will develop the first (pointwise) confidence intervals and hypothesis tests, as well as intervals and tests for the argmax of a concave treatment curve.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.

在现代数据环境中，使用非常灵活的统计方法，让数据“为自己说话”，而不是让研究人员对数据做出强有力的不合理的先验假设，这既是有利的，也是必要的。 不幸的是，这种灵活的方法通常需要从业者“调整”方法以获得可靠的结果。 这就给数据分析引入了一个特殊的元素，如果调整不当，这样的统计过程可能会返回错误的结果。 该项目的一个广泛主题是开发非常灵活且完全自动化的统计方法（依赖于凸性），这意味着它们不依赖于用户选择的调优参数。 另一个主题是研究非常灵活但有效的程序，用于在治疗变量是连续的（例如，“你的药物剂量是多少”，在治疗疾病的药物的设置中）而不是二元（“你是否接受了药物，是或否”）;它将使用第一个主题中的全自动方法，也在第二个主题中。 它将专注于超越估计和实际执行推理，这意味着它将量化估计的实际可靠性，以便它们可以用于政策/决策制定。 在因果关系设置中，它将考虑不同的例子，如护士工作时间对医院疗效的影响，临床测量，如BMI（身体质量指数）对健康结果的影响，或花在教育上的时间对职业结果的影响。 基于凸性的无参数调整过程在经济数据研究和运筹学中出现的优化问题中有许多用途。本项目集中于几个非标准统计问题，这些问题在现代数据设置中通过回答复杂问题而在实践中统一起来，并且在理论上通过具有非标准收敛率和经常的非正态极限分布而统一起来。研究者将考虑以下两个主要方面：（a）形状约束凸函数的非参数估计和推断，（B）对因果连续治疗效应曲线（基于观察数据）和相关参数进行非参数检验和/或置信区间。通常最好使用灵活的非参数方法，以便估计和推断产生可靠的结果，而不依赖于强有力的假设。不幸的是，大多数经典的非参数方法严重依赖于（可能有许多）调谐参数的选择，其选择可能具有挑战性。在这个项目中，研究人员将研究所谓的形状约束，这是非参数的，但也允许估计/推断，而不需要选择一个调谐参数。评估因果关系是科学探究中最基本但也最具挑战性的任务之一。对于观测数据，黄金标准是所谓的双重稳健估计，其中“双重稳健”意味着最佳有效。 研究者将开发第一个（逐点）置信区间和假设检验，以及凹处理曲线的argmax的区间和检验。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智力价值和更广泛的影响审查标准进行评估来支持。