Semiparametric Methods for Analysis of Complex Data

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In the era of big data, complex data naturally arise in modern scientific applications. For example, the advance in computation and technology has enabled the routine collection of high-frequency functional data and high-resolution images. Scientists are facing daunting challenges from the data, including the massive scale, intricate dependence structures, and various shape constraints that are vital for scientific interpretability. This project will develop new flexible methods for shape-constrained regression and high-dimensional quantile regression to comprehensively depict the dependence between variables, with a focus on providing scalable implementation and theoretically guaranteed inference. These tools will address pressing statistical and computational challenges, leading to broad applications in medicine, neuroscience, cancer-related studies, and industrial settings. The project will also develop and distribute open-source software and provide research opportunities for undergraduate and graduate students. The project will develop novel semiparametric methods for high-dimensional quantile regression and shape-constrained regression. The PI will investigate a paradigm shift in high-dimensional regression from a joint, iterative scheme to a two-step, distributed scheme. This strategy allows the utilization of parallel computation and is coupled with proper uncertainty propagation to ensure statistical optimality and frequentist coverage of simultaneous confidence and credible bands. Several regimes using functional and image data will be considered, for example, mean regression, quantile regression, and variable selection. The project will also develop new methods for nonparametric regression under shape constraints, including local sparsity and stationary points of unknown functions. The project will enrich the statistical toolbox to cope with complex data by developing a suite of semiparametric methods that are theoretically sound and computationally efficient.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.