is asymptotically efficient under the hypotheses of Theorem 12. Proof. Note that R0(F0) is a lower bound on the asymptotic risk of
by Theorem 12. Moreover,
by Chauchy-Schwartz inequality applied to
we have the result. Note that α > 1 is not admissible as at most Nn = n quantiles are of statistical interest.
Stefano M. Iacus, Davide La Torre