LEAPS-MPS: Getting modeling precision right for data with measurement errors

在许多领域收集的数据经常带有测量误差，例如经济调查中的家庭收入、自我报告的每日纤维摄入量以及流行病学研究中的辐射暴露剂量。该项目旨在为涉及测量误差的各种模型设置开发高效和可靠的统计工具。该研究将提高回归模型的估计精度，填补时间序列分析中模型检验的空白。所提出的方法的应用将促进对广泛领域的精确关系的理解，例如流行病学中膳食纤维摄入量与肠道微生物群之间的关系。该项目还将促进本科生和研究生，特别是来自代表性不足群体的学生，在数学和统计学方面的研究参与度。在统计建模中，忽略预测值中的测量误差往往会导致估计偏差和假设检验能力降低。该项目将在一大类模型中开发有效的估计和强大的测量误差测试程序，包括线性和非线性模型，病例对照研究中的广义线性模型，以及时间序列数据的自回归模型。所提出的估计和模型检验方法植根于基于加权经验残差过程的最小距离估计的稳健性、非参数估计技术的效率以及从外部对预测者的验证研究中提取信息的能力。这项研究不仅将建立所建议方法的理论，还将这些统计工具应用于真实世界的数据集，以帮助从业者更准确地理解潜在关系并得出更准确的结论。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。

Data are often collected with measurement errors in many areas such as household income from economic surveys, self-reported daily fiber intake, and the exposure dose to radiation in epidemiological studies. This project aims to develop efficient and robust statistical tools for various model settings involving measurement errors. The research will improve the estimation accuracy in regression models and fill the void in model-checking procedures for the time series analysis. The application of the proposed methods will advance the understanding of precise relationships in a wide variety of fields such as the relationship between dietary fiber intake and the gut microbiome in epidemiology. The project will also promote research engagement of both undergraduate and graduate students, especially students from underrepresented groups, in mathematics and statistics.In statistical modeling, ignoring the measurement error in predictors often causes estimation bias and lower hypothesis testing power. This project will develop efficient estimation and powerful testing procedures with measurement error in a broad class of models including linear and nonlinear models, generalized linear models in case-control studies, and autoregressive models for time series data. The proposed estimation and model-checking methods are rooted in the robustness of the minimum distance estimation based on the weighted empirical residual processes, the efficiency of the nonparametric estimation techniques, and the power of information extraction from external validation studies on predictors. This research will not only establish the theory of the proposed methodologies but also apply these statistical tools to real-world datasets to help practitioners understand the underlying relationships more accurately and draw more precise conclusions.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.