On the mean L¹-error in the heteroscedastic deconvolution problem with compactly supported noises

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

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G07
• 62G20

Acknowledgments

We would like to thank the reviewers for their kind and careful reading of the paper and for helpful comments and suggestions which led to this improved version.

Additional information

Funding

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) [grant number 101.02-2016.26].