High-dimensional simultaneous inference with the bootstrap

We propose a residual and wild bootstrap methodology for individual and simultaneous inference in high-dimensional linear models with possibly non-Gaussian and heteroscedastic errors. We establish asymptotic consistency for simultaneous inference for parameters in groups G, where p gg n, s0 = o(n1/2/log(p) log(|G|)1/2) and log(|G|) = o(n1/7), with p the number of variables, n the sample size and s0 denoting the sparsity. The theory is complemented by many empirical results. Our proposed procedures are implemented in the R-package hdi.