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Title:Inference of high-dimensional linear models with time-varying coefficients
Author(s):He, Yifeng
Director of Research:Chen, Xiaohui
Doctoral Committee Chair(s):Chen, Xiaohui
Doctoral Committee Member(s):Chen, Yuguo; Qu, Annie; Simpson, Douglas
Department / Program:Statistics
Discipline:Statistics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):High Dimension, Lasso, Ridge Regression, Time Series, Time Varying Coefficient Models, Kronecker, Precision Matrix, Graphical Methods, Graphical Lasso
Abstract: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.
Issue Date:2018-12-04
Type:Thesis
URI:http://hdl.handle.net/2142/102452
Rights Information:Copyright 2017 Yifeng He
Date Available in IDEALS:2019-02-06
Date Deposited:2018-12


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