  In this work, we construct a risk estimator for hard thresholding which can
be used as a basis to solve the difficult task of automatically selecting the
threshold. As hard thresholding is not even continuous, Stein's lemma cannot be
used to get an unbiased estimator of degrees of freedom, hence of the risk. We
prove that under a mild condition, our estimator of the degrees of freedom,
although biased, is consistent. Numerical evidence shows that our estimator
outperforms another biased risk estimator.
