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

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2019

Author dc:creator

• He, Yifeng

Contributors dc:contributor

• Chen, Xiaohui
• Chen, Yuguo
• Qu, Annie
• Simpson, Douglas

• High Dimension, Lasso, Ridge Regression, Time Series, Time Varying Coefficient Models, Kronecker, Precision Matrix, Graphical Methods, Graphical Lasso

Statement dc:rights

• Copyright 2017 Yifeng He

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/102452

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/102452