  Threshold selection is a fundamental problem in any threshold-based extreme
value analysis. While models are asymptotically motivated, selecting an
appropriate threshold for finite samples is difficult and highly subjective
through standard methods. Inference for high quantiles can also be highly
sensitive to the choice of threshold. Too low a threshold choice leads to bias
in the fit of the extreme value model, while too high a choice leads to
unnecessary additional uncertainty in the estimation of model parameters. We
develop a novel methodology for automated threshold selection that directly
tackles this bias-variance trade-off. We also develop a method to account for
the uncertainty in the threshold estimation and propagate this uncertainty
through to high quantile inference. Through a simulation study, we demonstrate
the effectiveness of our method for threshold selection and subsequent extreme
quantile estimation, relative to the leading existing methods, and show how the
method's effectiveness is not sensitive to the tuning parameters. We apply our
method to the well-known, troublesome example of the River Nidd dataset.
