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Remarks on extremal problems in nonparametric curve estimation

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  • Leonov, Sergei L.

Abstract

We discuss optimization problems which arise in various nonparametric statistical settings with Hölder function classes. We establish a new property of the solution of an optimal recovery problem which leads to exact constants in the formulas for asymptotic minimax risks.

Suggested Citation

  • Leonov, Sergei L., 1999. "Remarks on extremal problems in nonparametric curve estimation," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 169-178, June.
    • Handle: RePEc:eee:stapro:v:43:y:1999:i:2:p:169-178
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    References listed on IDEAS

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    1. Lepskii, O. V. & Spokoiny, V., 1995. "Optimal Pointwise Adaptive Methods in Nonparametric Estimation," SFB 373 Discussion Papers 1995,22, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Lepski, O. & Tsybakov, A., 1996. "Asymptotically exact nonparametric hypothesis testing in sup-norm and at a fixed point," SFB 373 Discussion Papers 1996,91, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    Cited by:

    1. GaI¨ffas, Stéphane, 2007. "Sharp estimation in sup norm with random design," Statistics & Probability Letters, Elsevier, vol. 77(8), pages 782-794, April.

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