Convergence Rates of Density Estimation in Besov Spaces

Huiying Wang

doi:10.4236/am.2011.210175

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Convergence Rates of Density Estimation in Besov Spaces

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DOI: 10.4236/am.2011.210175 3,819 Downloads 6,445 Views Citations

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Huiying Wang

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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

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

References

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[2]	D. L. Donoho, I. M. Johnstone, G. Kerkyacharian and D. Picard, “Den-sity Estimation by Wavelet Thresholding,” The Annals of Statistics, Vol. 24, No. 2, 1996, pp. 508-539. doi:10.1214/aos/1032894451

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