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On minimax convergence rates under Lp-risk for the anisotropic functional deconvolution model

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  • Benhaddou, Rida

Abstract

We look into minimax results for the anisotropic functional deconvolution model under the Lp-risk, 1≤p<∞. We construct lower bounds and show that the wavelet hard-thresholding estimator is asymptotically near-optimal in the Lp-risk.

Suggested Citation

  • Benhaddou, Rida, 2017. "On minimax convergence rates under Lp-risk for the anisotropic functional deconvolution model," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 120-125.
    • Handle: RePEc:eee:stapro:v:130:y:2017:i:c:p:120-125
    DOI: 10.1016/j.spl.2017.07.008
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    References listed on IDEAS

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    1. Petsa, Athanasia & Sapatinas, Theofanis, 2009. "Minimax convergence rates under the Lp-risk in the functional deconvolution model," Statistics & Probability Letters, Elsevier, vol. 79(13), pages 1568-1576, July.
    2. Petsa, Athanasia & Sapatinas, Theofanis, 2009. "Erratum to: "Minimax convergence rates under the Lp-risk in the functional deconvolution model" [Statist. Probab. Lett. 79 (2009) 1568-1576]," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1890-1890, September.
    3. Iain M. Johnstone & Gérard Kerkyacharian & Dominique Picard & Marc Raimondo, 2004. "Wavelet deconvolution in a periodic setting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 547-573, August.
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