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2013 Wavelet Optimal Estimations for Density Functions under Severely Ill-Posed Noises
Rui Li, Youming Liu
Abstr. Appl. Anal. 2013(SI32): 1-7 (2013). DOI: 10.1155/2013/260573


Motivated by Lounici and Nickl's work (2011), this paper considers the problem of estimation of a density f based on an independent and identically distributed sample Y 1 , , Y n from g = f * φ . We show a wavelet optimal estimation for a density (function) over Besov ball B r , q s ( L ) and L p risk ( 1 p < ) in the presence of severely ill-posed noises. A wavelet linear estimation is firstly presented. Then, we prove a lower bound, which shows our wavelet estimator optimal. In other words, nonlinear wavelet estimations are not needed in that case. It turns out that our results extend some theorems of Pensky and Vidakovic (1999), as well as Fan and Koo (2002).


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Rui Li. Youming Liu. "Wavelet Optimal Estimations for Density Functions under Severely Ill-Posed Noises." Abstr. Appl. Anal. 2013 (SI32) 1 - 7, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1306.62095
MathSciNet: MR3143555
Digital Object Identifier: 10.1155/2013/260573

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI32 • 2013
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