  We propose randomization tests of whether forecast 1 outperforms forecast 2
across a class of scoring functions. This hypothesis is of applied interest:
While the prediction context often prescribes a certain class of scoring
functions, it is typically hard to motivate a specific choice on statistical or
substantive grounds. We investigate the asymptotic behavior of the test
statistics under mild conditions, avoiding the need to assume particular
dynamic properties of forecasts and realizations. The properties of the
one-sided tests depend on a corresponding version of Anderson's inequality,
which we state as a conjecture of independent interest. Numerical experiments
and a data example indicate that the tests have good size and power properties
in practically relevant situations.
