University of Illinois Urbana-Champaign

Inference of high-dimensional linear models with time-varying coefficients

He, Yifeng

Content Files
HE-DISSERTATION-2018.pdf

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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
Date of Ingest
2019-02-06T19:36:21Z
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.
Graduation Semester
2018-12
Type of Resource
text
Permalink
http://hdl.handle.net/2142/102452
Copyright and License Information
Copyright 2017 Yifeng He

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