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

[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.

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