Inference of high-dimensional linear models with time-varying coefficients
He, Yifeng
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https://hdl.handle.net/2142/102452
Description
Title
Inference of high-dimensional linear models with time-varying coefficients
Author(s)
He, Yifeng
Issue Date
2018-12-04
Director of Research (if dissertation) or Advisor (if thesis)
Chen, Xiaohui
Doctoral Committee Chair(s)
Chen, Xiaohui
Committee Member(s)
Chen, Yuguo
Qu, Annie
Simpson, Douglas
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(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.
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