Nonparametric regression on the hyper-sphere with uniform design

• Autores: Jean-Baptiste Monnier
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 20, Nº. 2, 2011, págs. 412-446
• Idioma: inglés
• DOI: 10.1007/s11749-011-0233-7
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• Resumen

  • This paper deals with the estimation of a function f defined on the sphere Sd of ℝd+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 ⊛ and f★ 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 ⊛ outperforms f★ , and run finite-sample simulations with f ⊛ 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.