Bootstrapping kernel spectral density estimates with kernel bandwidth estimation

We address the problem of confidence interval estimation of spectral densities using the bootstrap. Of special interest is the choice of the kernel global bandwidth. First, we investigate resampling based techniques for the choice of the bandwidth. We then address the question of whether the accuracy of the distributional bootstrap estimation is influenced by using the resample version, rather than the sample version of an empirical bandwidth. Aligned with recent results on non-parametric probability density estimation, we found that varying an empirical bandwidth across resamples is largely unnecessary and thus, the computational burden is greatly reduced while maintaining estimation accuracy.