bibkey: micchellirivlin1977optimalrecovery authors: C. A. Micchelli and T. J. Rivlin year: 1977 title: A Survey of Optimal Recovery doi: 10.1007/978-1-4684-2388-4_1 url: https://doi.org/10.1007/978-1-4684-2388-4_1 claim: Worst-case recovery from incomplete information and the radius of a compatible set. strata_touched: [] license: citation-only triage: anchor

A Survey of Optimal Recovery

For a scalar target, the midpoint of the infimum and supremum of a nonempty bounded compatible set has error at most half its diameter. This is a classical optimal-recovery principle.

PointwiseMinimaxUpper applies that principle to finite atomic probability laws and arbitrary pointwise noisy Laplace observations. The estimator has no computational restriction. The analytic diameter bound comes from the separation-free endpoint interpolation certificates. The resulting constant 1024 Ehi/eta^2 and its joint dimension-precision rate are repository-derived; this reference is not claimed to prove those analytic bounds.

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• DOI: 10.1007/978-1-4684-2388-4_1
• URL: https://doi.org/10.1007/978-1-4684-2388-4_1
• Crossref record: https://api.crossref.org/works/10.1007/978-1-4684-2388-4_1

The DOI resolves to the Springer chapter A Survey of Optimal Recovery by C. A. Micchelli and T. J. Rivlin. Publisher metadata and Crossref agree on the title, authors, DOI and 1977 publication year; Crossref places the chapter in Optimal Estimation in Approximation Theory, Springer US, pages 1–54.

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