2018/03/17 by Juditsky, Anatoli, Nemirovski, Arkadi
#62C20 #62G05 #62H12 #FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1803.06446
We consider the problem of recovering linear image of unknown signal belonging to a given convex compact signal set from noisy observation of another linear image of the signal. We develop a simple generic efficiently computable nonlinear in observations "polyhedral" estimate along with computation-friendly techniques for its design and risk analysis. We demonstrate that under favorable circumstances the resulting estimate is provably near-optimal in the minimax sense, the "favorable circumstances" being less restrictive than the weakest known so far assumptions ensuring near-optimality of estimates which are linear in observations.