Non-parametric regression on the hyper-sphere with uniform design

Abstract : This paper deals with the estimation of a function $f$ defined on the sphere $\Sp^d$ of $\R^{d+1}$ from a sample of noisy observation points. We introduce an estimation procedure based on wavelet-like functions on the sphere called needlets and study two estimators $f^\circledast$ and $f^\bigstar$ respectively made adaptive through the use of a stochastic and deterministic needlet-shrinkage method. We show hereafter that these estimators are nearly-optimal in the minimax framework, explain why $f^\circledast$ outperforms $f^\bigstar$ and run finite sample simulations with $f^\circledast$ to demonstrate that our estimation procedure is easy to implement and fares well in practice. We are motivated by applications in geophysical and atmospheric sciences.
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Test Publication, 2011, 20 (2), pp.412-446. <10.1007/s11749-011-0233-7>
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Contributeur : Jean-Baptiste Monnier <>
Soumis le : jeudi 6 janvier 2011 - 11:53:59
Dernière modification le : mardi 11 octobre 2016 - 15:20:34
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Jean-Baptiste Monnier. Non-parametric regression on the hyper-sphere with uniform design. Test Publication, 2011, 20 (2), pp.412-446. <10.1007/s11749-011-0233-7>. <hal-00552982>

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