![](/images/graphics-bg.png)
Optimal Wavelet Estimation of Density Derivatives for Size-Biased Data
Joint Authors
Wang, Jinru
Geng, Zijuan
Jin, Fengfeng
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-01-30
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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 ) ∈ B r , q s ( A , L ) attains the optimal covergence rate when r ≥ p , and the nonlinear one E ( ∥ f ^ lin ( m ) - f ( m ) ∥ p ) does the same if r < p .
American Psychological Association (APA)
Wang, Jinru& Geng, Zijuan& Jin, Fengfeng. 2014. Optimal Wavelet Estimation of Density Derivatives for Size-Biased Data. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-1014135
Modern Language Association (MLA)
Wang, Jinru…[et al.]. Optimal Wavelet Estimation of Density Derivatives for Size-Biased Data. Abstract and Applied Analysis No. 2014 (2014), pp.1-13.
https://search.emarefa.net/detail/BIM-1014135
American Medical Association (AMA)
Wang, Jinru& Geng, Zijuan& Jin, Fengfeng. Optimal Wavelet Estimation of Density Derivatives for Size-Biased Data. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-1014135
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1014135