Optimal Wavelet Estimation of Density Derivatives for Size-Biased Data
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 i...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/512634 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832554254701690880 |
|---|---|
| author | Jinru Wang Zijuan Geng Fengfeng Jin |
| author_facet | Jinru Wang Zijuan Geng Fengfeng Jin |
| author_sort | Jinru Wang |
| collection | DOAJ |
| description | 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 r≥p, and the nonlinear one E(∥f^lin(m)-f(m)∥p) does the same if r<p. |
| format | Article |
| id | doaj-art-daa5747f1e654fec8c0f94ad74ae3cc2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-daa5747f1e654fec8c0f94ad74ae3cc22025-02-03T05:52:06ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/512634512634Optimal Wavelet Estimation of Density Derivatives for Size-Biased DataJinru Wang0Zijuan Geng1Fengfeng Jin2Department of Applied Mathematics, Beijing University of Technology, Beijing 100124, ChinaDepartment of Applied Mathematics, Beijing University of Technology, Beijing 100124, ChinaDepartment of Applied Mathematics, Beijing University of Technology, Beijing 100124, ChinaA 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 r≥p, and the nonlinear one E(∥f^lin(m)-f(m)∥p) does the same if r<p.http://dx.doi.org/10.1155/2014/512634 |
| spellingShingle | Jinru Wang Zijuan Geng Fengfeng Jin Optimal Wavelet Estimation of Density Derivatives for Size-Biased Data Abstract and Applied Analysis |
| title | Optimal Wavelet Estimation of Density Derivatives for Size-Biased Data |
| title_full | Optimal Wavelet Estimation of Density Derivatives for Size-Biased Data |
| title_fullStr | Optimal Wavelet Estimation of Density Derivatives for Size-Biased Data |
| title_full_unstemmed | Optimal Wavelet Estimation of Density Derivatives for Size-Biased Data |
| title_short | Optimal Wavelet Estimation of Density Derivatives for Size-Biased Data |
| title_sort | optimal wavelet estimation of density derivatives for size biased data |
| url | http://dx.doi.org/10.1155/2014/512634 |
| work_keys_str_mv | AT jinruwang optimalwaveletestimationofdensityderivativesforsizebiaseddata AT zijuangeng optimalwaveletestimationofdensityderivativesforsizebiaseddata AT fengfengjin optimalwaveletestimationofdensityderivativesforsizebiaseddata |