Nonparametric Estimation and Inference with Network Data

网络数据在统计、社会、行为和生物医学科学中无处不在。这种类型的相关数据捕捉研究单位之间的互动，例如公司之间的产出、国家之间的贸易或政客之间的筹款。如今，基于网络的信息被广泛用于测试特定领域的假设以及数据和决策科学中的决策。然而，在实证工作中，网络数据的显著激增并没有伴随着指导其正确使用并提供有效的估计和推断程序的统计方法的完整发展。目前使用网络数据的实践受到文献中少数几个结果的限制，许多具有实际意义的估计和推断问题仍然没有解决。在这个项目中，调查人员试图利用二元数据对非参数和半参数统计方法进行全面研究，这些数据是按两国之间的贸易等单位对索引的数据。所建立的方法和理论将作为分析更一般的网络数据的基础。研究人员计划开发通用软件来实施主要的理论和方法结果。该项目将为研究生提供培训机会。研究将集中在使用二进网络数据的非参数和半参数估计和推断方法上，由于其固有的缺乏统计独立性，这带来了特定的技术挑战。该项目的最终目标是开发全面的大样本近似，导致函数估计的最佳和/或稳健的点估计和统计推断程序，将密度函数和回归函数作为特例包括在内。为此，研究人员将发展新的随机过程的强逼近结果，然后将其应用于基于二进网络数据的函数统计分布的近似。还将建立使用网络数据的不同非参数/半参数估计量的最小最大最优一致收敛速度。然后，主要的理论结果将被应用于依赖网络数据的半参数估计。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Network data is ubiquitous in the statistical, social, behavioral, and biomedical sciences. This type of dependent data captures interactions between the units of study, such as output between firms, trade between countries, or fundraising between politicians. Network-based information is widely used nowadays for both testing domain-specific hypotheses and policy-making decisions in data and decision sciences. However, the remarkable proliferation of network data in empirical work has not been accompanied by a complete development of statistical methods guiding its correct use and providing valid estimation and inference procedures. Current practice employing network data is limited by the few results available in the literature, and many estimation and inference problems of practical importance remain unresolved. In this project, the investigators seek to undertake a comprehensive study of non-parametric and semi-parametric statistical methods employing dyadic data, data indexed by pairs of units such as trade between two countries. The established methods and theory will serve as a building block for the analysis of more general network data. The investigators plan to develop general-purpose software to implement the main theoretical and methodological results. The project will provide training opportunities for graduate students.The research will focus on non-parametric and semi-parametric estimation and inference methods employing dyadic network data, which poses specific technical challenges due to its inherent lack of statistical independence. The project's ultimate goal is to develop comprehensive large-sample approximations leading to optimal and/or robust point estimation and statistical inference procedures for functional estimation, covering density and regression functions as special cases. To this end, the investigators will develop novel strong approximation results for stochastic processes, which will then be deployed to approximate the distribution of functional statistics based on dyadic network data. Minimax optimal uniform convergence rates for different non-/semi-parametric estimators using network data will also be established. The main theoretical results will then be applied to semiparametric estimation relying on network data.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.