Open Access
2014 Optimal Wavelet Estimation of Density Derivatives for Size-Biased Data
Jinru Wang, Zijuan Geng, Fengfeng Jin
Abstr. Appl. Anal. 2014: 1-13 (2014). DOI: 10.1155/2014/512634


A perfect achievement has been made for wavelet density estimation by Dohono et al. in 1996, when the samples without any noise are independent and identically distributed (i.i.d.). But in many practical applications, the random samples always have noises, and estimation of the density derivatives is very important for detecting possible bumps in the associated density. Motivated by Dohono's work, we propose new linear and nonlinear wavelet estimators f^lin(m),f^non(m) for density derivatives f(m) when the random samples have size-bias. It turns out that the linear estimation E(∥f^lin(m)-f(m)p) for f(m)Br,qs(A,L) attains the optimal covergence rate when rp, and the nonlinear one E(∥f^lin(m)-f(m)p) does the same if r<p.


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Jinru Wang. Zijuan Geng. Fengfeng Jin. "Optimal Wavelet Estimation of Density Derivatives for Size-Biased Data." Abstr. Appl. Anal. 2014 1 - 13, 2014.


Published: 2014
First available in Project Euclid: 26 March 2014

zbMATH: 07022523
MathSciNet: MR3166625
Digital Object Identifier: 10.1155/2014/512634

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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