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Chen, Xiaohui Chen, Xiaohui Chen, Yuguo Qu, Annie Simpson, Douglas He, Yifeng 2019-02-06T19:36:21Z 2019-02-06T19:36:21Z 2018-12-04 2018-12 In part 1, we propose a pointwise inference algorithm for high-dimensional linear models with time-varying coefficients and dependent error processes. The method is based on a novel combination of the nonparametric kernel smoothing technique and a Lasso bias-corrected ridge regression estimator using a bias-variance decomposition to address non-stationarity in the model. A hypothesis testing setup with familywise error control is presented alongside synthetic data and a real application to fMRI data for Parkinson's disease. In part 2, we propose an algorithm for covariance and precision matrix estimation high-dimensional transpose-able data. The method is based on a Kronecker product approximation of the graphical lasso and the application of the alternating directions method of multipliers minimization. A simulation example is provided. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-02-05 without embargo terms The student, Yifeng He, accepted the attached license on 2018-12-03 at 14:55. The student, Yifeng He, submitted this Dissertation for approval on 2018-12-03 at 15:10. This Dissertation was approved for publication on 2018-12-04 at 10:43. DSpace SAF Submission Ingestion Package generated from Vireo submission #13143 on 2019-02-05 at 11:12:59 Made available in DSpace on 2019-02-06T19:36:21Z (GMT). No. of bitstreams: 2 HE-DISSERTATION-2018.pdf: 942235 bytes, checksum: b3b5d33043e8ae26c47be3f9f0665b25 (MD5) LICENSE.txt: 4206 bytes, checksum: 77c750dc7bf40b8a4c4afb3c869021cf (MD5) Previous issue date: 2018-12-04 application/pdf http://hdl.handle.net/2142/102452 en Copyright 2017 Yifeng He High Dimension, Lasso, Ridge Regression, Time Series, Time Varying Coefficient Models, Kronecker, Precision Matrix, Graphical Methods, Graphical Lasso Inference of high-dimensional linear models with time-varying coefficients text text Statistics Statistics University of Illinois at Urbana-Champaign Dissertation Ph.D.