Work

Adaptive Wavelet Estimations in the Convolution Structure Density Model

Year: 2020

Type: article

Abstract: Using kernel methods, Lepski and Willer study a convolution structure density model and establish adaptive and optimal Lp risk estimations over an anisotropic Nikol’skii space (Lepski, O.; Willer, T. Oracle inequalities and adaptive estimation in the convolution structure density model. Ann. Stat.2019, 47, 233–287). Motivated by their work, we consider the same problem over Besov balls by wavelets in this paper and first provide a linear wavelet estimate. Subsequently, a non-linear wavelet estimator is introduced for adaptivity, which attains nearly-optimal convergence rates in some cases.

Source: Mathematics

DOI: 10.3390/math8091391

Authors: Kaikai Cao, Xiaochen Zeng

Institutions: Weifang University, Beijing University of Technology

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,267

Funder: National Natural Science Foundation of China