  This note addresses the question of optimally estimating a linear functional
of an object acquired through linear observations corrupted by random noise,
where optimality pertains to a worst-case setting tied to a symmetric, convex,
and closed model set containing the object. It complements the article
"Statistical Estimation and Optimal Recovery" published in the Annals of
Statistics in 1994. There, Donoho showed (among other things) that, for
Gaussian noise, linear maps provide near-optimal estimation schemes relatively
to a performance measure relevant in Statistical Estimation. Here, we advocate
for a different performance measure arguably more relevant in Optimal Recovery.
We show that, relatively to this new measure, linear maps still provide
near-optimal estimation schemes even if the noise is merely log-concave. Our
arguments, which make a connection to the deterministic noise situation and
bypass properties specific to the Gaussian case, offer an alternative to parts
of Donoho's proof.
