UCLA

In terms of constructing confidence intervals for coefficients in high-dimensional linear models under group norm regularization, the standard residual bootstrap method has been proven to be inconsistent and its performance is unstable especially for coefficients in active groups. In this thesis, we consider a thresholding method which forces the close-to-zero estimated coefficients to be exact zero. Through simulations, this method outperforms the standard method in terms of the confidence interval coverage rate. Instead of setting a hard threshold on $\hat{\beta}$, we also consider a method which selects groups with high chance of being active in multiple simulated datasets. After thresholding, two other confidence interval building methods are proposed, and in this thesis, these three methods are compared in terms of coverage rate for both active groups and non-active groups under different conditions. Modified thresholding confidence interval construction method is most consistent and accurate method based on the simulation results.