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On sharp nonparametric estimation of differentiable functions

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  • Efromovich, Sam

Abstract

Sharp minimax nonparametric estimation is well known for functions from a Sobolev ellipsoid which is defined via Fourier coefficients of differentiable functions with specific boundary conditions. The theory is based on a renown lower bound of Pinsker (1980) and an adaptive estimator that attains it. This paper solves a long-standing problem of adaptive estimation without assuming boundary conditions.

Suggested Citation

  • Efromovich, Sam, 2019. "On sharp nonparametric estimation of differentiable functions," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 9-14.
    • Handle: RePEc:eee:stapro:v:152:y:2019:i:c:p:9-14
    DOI: 10.1016/j.spl.2019.04.007
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