Digital Commons Network^™

A Comparison Of Inference Methods In High-Dimensional Linear Regression, Imtiaz Ebna Mannan

Theses and Dissertations

Building confidence/credible intervals for the high-dimensional (p >> n) linear models have been the subject of exploration for many years. In this paper, we explore three specific setups. First, we look at the Bayesian paradigm for the LASSO model. A double-exponential prior has been applied to the regression coefficient and from that, a posterior distribution is derived to get the necessary quantiles to calculate the credible intervals for the regression coefficients. Second, we explore the de-sparsified LASSO estimates, and using its asymptotic normality, we calculate the confidence intervals for the model coefficients. Finally, we incorporate an adaptive LASSO model. To …