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

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

He, Yifeng

关键词: High Dimension, Lasso, Ridge Regression, Time Series, Time Varying Coefficient Models, Kronecker, Precision Matrix, Graphical Methods, Graphical Lasso;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/102452/HE-DISSERTATION-2018.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.