We explore the evaluation (ranking) of point forecasts by a “stochastic loss distance” (SLD) criterion, under which we prefer forecasts with loss distributions F(L(e)) “close” to the unit step function at 0. We show that, surprisingly, ranking by SLD corresponds to ranking by expected loss.

In this note, I extend the optimal asymptotic least squares estimation framework to deal with singularities in the asymptotic covariance of the distance function. Further, the relationship between the asymptotic least squares and maximum likelihood estimation frameworks in such a singular set-up...