A Data-Driven Wavelet Estimator For Deconvolution Density Estimations

This current paper provides a data-driven wavelet estimator for deconvolution density model. Moreover, we investigate the totally adaptive estimations with moderately ill-posed noises over L-p risk on Besov spaces B-r,q(s)(R). Compared with the traditional adaptive wavelet estimators, the estimation for the case of 0 < s <= 1/r is considered. On the other hand, the convergence rate in the region of 1 <= p <= 2sr+(2 beta+1)r/sr+2 beta+1 is improved than that for not necessarily compactly supported density estimations.

Automated summary

This paper proposes a data-driven wavelet estimator for deconvolution density model. Additionally, we investigate the totally adaptive estimations with moderately ill-posed noises on Besov spaces B-r,q(s)(R). The estimation for the case of 0 < s <= 1/r is considered, and the convergence rate in the region of 1 <= p <= 2sr+(2 beta+1)r/sr+2 beta+1 is improved compared to not necessarily compactly supported density estimations.