Convergence Rates of Density Estimation in Besov Spaces

Huiying Wang

doi:10.4236/am.2011.210175

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Applied Mathematics > Vol.2 No.10, October 2011

Convergence Rates of Density Estimation in Besov Spaces ()

Huiying Wang

DOI: 10.4236/am.2011.210175 PDF HTML 3,963 Downloads 6,591 Views Citations

Abstract

The optimality of a density estimation on Besov spaces B^s_r,q(R) for the L_p 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 R_n(B^s_r,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.

Keywords

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

Share and Cite:

H. Wang, "Convergence Rates of Density Estimation in Besov Spaces," Applied Mathematics, Vol. 2 No. 10, 2011, pp. 1258-1262. doi: 10.4236/am.2011.210175.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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