Near-optimal recovery of linear and N-convex functions on unions of convex sets

@article{Juditsky2019NearoptimalRO,
  title={Near-optimal recovery of linear and N-convex functions on unions of convex sets},
  author={Anatoli B. Juditsky and Arkadi Nemirovski},
  journal={Information and Inference: A Journal of the IMA},
  year={2019}
}
In this paper we build provably near-optimal, in the minimax sense, estimates of linear forms and, more generally, ‘$N$-convex functionals’ (an example being the maximum of several fractional-linear functions) of unknown ‘signal’ from indirect noisy observations, the signal assumed to belong to the union of finitely many given convex compact sets. Our main assumption is that the observation scheme in question is good in the sense of Goldenshluger et al. (2015, Electron. J. Stat., 9, 1645–1712… Expand

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