Shape-constrained Regression and False Discovery Rate Control for Functional Data with Applications to Human Intracranial Electroencephalography Study
| dc.contributor.advisor | Li, Meng | |
| dc.creator | Wang, Zhengjia | |
| dc.date.accessioned | 2022-10-11T19:22:30Z | |
| dc.date.available | 2022-10-11T19:22:30Z | |
| dc.date.created | 2021-08 | |
| dc.date.issued | 2021-06-22 | |
| dc.date.submitted | August 2021 | |
| dc.date.updated | 2022-10-11T19:22:30Z | |
| dc.description.abstract | Abstract: Intracranial electroencephalography (iEEG) is a neuroscience technique that allows for recordings of human brain activity with high spatial and temporal resolution. Since iEEG data consists of continuous recordings of voltage signals from electrodes at different brain locations, functional data analysis (FDA) could be a useful tool for transforming iEEG data into meaningful discoveries about brain function. Shape constraints that arise from domain knowledge are crucial for a flexible nonparametric model to be interpretable. This thesis advances methods, theory, computation, and visualization for functional data of complex dependent structure with shape constraints by addressing statistical questions raised by the application of FDA to iEEG data. The first project focuses on locally sparse regression functions and develops a weighted group bridge approach for simultaneous function estimation and support recovery in function-on-scalar mixed effect models. We use locally supported B-splines to transform nonparametric functions to vectors of diverging dimension with group sparsity, and propose a fast non-convex optimization algorithm using nested alternative direction method of multipliers for estimation. We show that the estimated coefficient functions achieve the minimax optimal rate and resemble a phase transition phenomenon. For support estimation, we establish selection consistency under approximate sparsity and provide a simple sufficient regularity condition for strict selection consistency. The second project controls the false discovery rate (FDR) for a continuum of hypotheses related to functional data. A key contribution of this project is a set-theoretic framework to embed topological constraints such as the connectedness of significant regions into a two-stage multiple testing procedure. In the first stage, we discover significant clusters by controlling a newly proposed extended false cluster rate criterion that allows for overlapped clusters. In the second stage, we control the FDR for individual hypotheses by post-selection inference based on derived conditional p-values given the rejected clusters in the first stage. We propose a testing procedure that reduces the number of unique tests from uncountably infinite to possibly linear in the number of discrete observations sampled from functional data, substantially facilitating the computation. We show that the FDR is controlled asymptotically at both the cluster and individual levels. In simulations to assess finite sample performance, the proposed methods compare favorably to several recently proposed methods. Methods developed in the first two projects are applied to iEEG data to study multisensory integration in the human brain. The third project develops the software package RAVE ("R" Analysis and Visualization of iEEG data). RAVE performs all of the steps necessary to analyze iEEG data, producing publication-ready graphics with an easy-to-use graphical user interface, using statistically valid analyses. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.citation | Wang, Zhengjia. "Shape-constrained Regression and False Discovery Rate Control for Functional Data with Applications to Human Intracranial Electroencephalography Study." (2021) Diss., Rice University. <a href="https://hdl.handle.net/1911/113691">https://hdl.handle.net/1911/113691</a>. | |
| dc.identifier.uri | https://hdl.handle.net/1911/113691 | |
| dc.language.iso | eng | |
| dc.rights | Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. | |
| dc.subject | Functional data analysis | |
| dc.subject | shape-constrained regression | |
| dc.subject | group-bridge penalty | |
| dc.subject | functional multiple testing | |
| dc.subject | false overlapped cluster rate | |
| dc.subject | FDR control | |
| dc.subject | iEEG | |
| dc.subject | rave | |
| dc.title | Shape-constrained Regression and False Discovery Rate Control for Functional Data with Applications to Human Intracranial Electroencephalography Study | |
| dc.type | Thesis | |
| dc.type.material | Text | |
| thesis.degree.department | Statistics | |
| thesis.degree.discipline | Engineering | |
| thesis.degree.grantor | Rice University | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Doctor of Philosophy |
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