A pointwise lower bound for generalized deconvolution density estimation

Abstract

This current paper considers a pointwise lower bound for generalized deconvolution density estimation under the local Hölder condition. Our result can be considered as extensions of the deconvolution density estimation and the classical density estimation with no errors. In addition, we do not assume that the noises are identically distributed in this paper.

Keywords:

• Generalized deconvolution
• lower bound
• density estimation
• wavelet
• unidentical errors

2010 MS Classifications:

• 41A25
• 41A27
• 62G07
• 42C40

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Nos. 11901019 and 11771030), the Beijing Natural Science Foundation (No. 1172001), the Beijing Postdoctoral Research Foundation (No. ZZ2019-77) and the Fundamental Research Fund of Beijing University of Technology (Nos. 006000546319511, 006000546319528).