Wavelet Optimal Estimations for Density Functions under Severely Ill-Posed Noises
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 Y1,…,Yn from g=f*φ. We show a wavelet optimal estimation for a density (function) over Besov ball Br,qs(L) and Lp risk (1≤p<...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/260573 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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 Y1,…,Yn
from g=f*φ. We show a wavelet optimal estimation for a density (function) over Besov ball Br,qs(L) and Lp 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). |
|---|---|
| ISSN: | 1085-3375 1687-0409 |