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

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.