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P. Baldi, G. Ker-kyacharian, D. Marinucci and D. Picard, “Adaptive Den-sity Estimation for Directional Data Using Needlets,” The Annals of Statistics, Vol. 37, No. 6A, 2009, pp. 3362-3395. doi:10.1214/09-AOS682

has been cited by the following article:

• TITLE: Convergence Rates of Density Estimation in Besov Spaces

  AUTHORS: Huiying Wang

  KEYWORDS: Optimal Rate of Convergence, Density Estimation, Besov Spaces, Wavelets

  JOURNAL NAME: Applied Mathematics, Vol.2 No.10, October 14, 2011

  ABSTRACT: The optimality of a density estimation on Besov spaces Bsr,q(R) for the Lp risk was established by Donoho, Johnstone, Kerkyacharian and Picard (“Density estimation by wavelet thresholding,” The Annals of Statistics, Vol. 24, No. 2, 1996, pp. 508-539.). To show the lower bound of optimal rates of convergence Rn(Bsr,q, p), they use Korostelev and Assouad lemmas. However, the conditions of those two lemmas are difficult to be verified. This paper aims to give another proof for that bound by using Fano’s Lemma, which looks a little simpler. In addition, our method can be used in many other statistical models for lower bounds of estimations.