Convergence Rates of Density Estimation in Besov Spaces
Huiying Wang
DOI: 10.4236/am.2011.210175   PDF    HTML     4,265 Downloads   7,185 Views   Citations


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.

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Wang, H. (2011) Convergence Rates of Density Estimation in Besov Spaces. Applied Mathematics, 2, 1258-1262. doi: 10.4236/am.2011.210175.

Conflicts of Interest

The authors declare no conflicts of interest.


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