Nonparametric confidence regions via the analytic wild bootstrap

Abstract

AbstractThe wild bootstrap is a nonparametric tool that can be used to estimate a sampling distribution in the presence of heteroscedastic errors. In particular, the wild bootstrap enables us to compute confidence regions for regression parameters under non‐i.i.d. models. While the wild bootstrap may perform well in these settings, its obvious drawback is a lack of computational efficiency. The wild bootstrap requires a large number of bootstrap replications, making the use of this tool impractical when dealing with big data. We introduce the analytic wild bootstrap (ANWB), which provides a nonparametric alternative way of constructing confidence regions for regression parameters. The ANWB is superior to the wild bootstrap from a computational standpoint while exhibiting similar finite‐sample performance. We report simulation results for both least squares and ridge regression. Additionally, we test the ANWB on a real dataset and compare its performance with that of other standard approaches.