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获研究单位之间的相互作用，例如公司之间的产出，国家之间的贸易或政治家之间的筹款。基于网络的信息如今被广泛用于测试特定领域的假设和数据和决策科学中的决策。然而，在实证工作中，网络数据的显着扩散并没有伴随着统计方法的完整发展，指导其正确使用，并提供有效的估计和推理程序。目前的做法，采用网络数据是有限的，在文献中提供的结果很少，许多估计和推理问题的实际重要性仍未得到解决。在这个项目中，调查人员试图采用二元数据，即按两个单位（如两国之间的贸易）编制索引的数据，对非参数和半参数统计方法进行全面研究。建立的方法和理论将作为一个积木更一般的网络数据的分析。研究人员计划开发通用软件来实现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元网络数据的非参数和半参数估计和推断方法，由于其固有的统计独立性不足，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值，从而为函数估计提供最佳和/或稳健的点估计和统计推断程序，包括密度和回归函数作为特殊情况。为此，研究人员将为随机过程开发新的强近似结果，然后将其部署到基于二元网络数据的函数统计分布中。还将建立使用网络数据的不同非/半参数估计的极小极大最优一致收敛速度。该奖项反映了NSF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。

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.