|
|||||
|
|
On the mean L1-error in the heteroscedastic deconvolution problem with compactly supported noises |
|
| Authors: | Cao Xuan Phuong Dang Duc Trong Tran Quoc Viet |
| Affiliation: | 1. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;2. Faculty of Mathematics and Computer Science, University of Science, Vietnam National University Ho Chi Minh City, Ho Chi Minh City, Vietnamcaoxuanphuong@tdt.edu.vn;4. Faculty of Mathematics and Computer Science, University of Science, Vietnam National University Ho Chi Minh City, Ho Chi Minh City, Vietnam;5. Centre for Mathematical Science, University of Science, Vietnam National University Ho Chi Minh City, Ho Chi Minh City, Vietnam |
| Abstract: | We study the heteroscedastic deconvolution problem when random noises have compactly supported densities. In this context, the Fourier transforms of the densities can vanish on the real line. We propose a truncated type of estimator for target density and derive the convergence rate of the mean L1-error uniformly over a class of target densities. A lower bound for the mean L1-error is also established. Some simulations will be given to illustrate the performance of the proposed estimator. |
| Keywords: | Compactly supported noises Convergence rate Estimator Heteroscedastic noises |