  This paper contributes to answering a question that is of crucial importance
in risk management and extreme value theory: How to select the threshold above
which one assumes that the tail of a distribution follows a generalized Pareto
distribution. This question has gained increasing attention, particularly in
finance institutions, as the recent regulative norms require the assessment of
risk at high quantiles. Recent methods answer this question by multiple uses of
the standard goodness-of-fit tests. These tests are based on a particular
choice of symmetric weighting of the mean square error between the empirical
and the fitted tail distributions. Assuming an asymmetric weighting, which
rates high quantiles more than small ones, we propose new goodness-of-fit tests
and automated threshold selection procedures. We consider a parameterized
family of asymmetric weight functions and calculate the corresponding mean
square error as a loss function. We then explicitly determine the risk function
as the finite sample expected value of the loss function. Finally, the risk
function can be used to discuss the question of which symmetric or asymmetric
weight function and, thus, which goodness-of-fit test should be used in a new
method for determining the threshold value.
