Adaptive Wavelet Estimations in the Convolution Structure Density Model - Kaikai Cao; Xiaochen Zeng (Mathematics, 2020)
Using kernel methods, Lepski and Willer study a convolution structure density model and establish adaptive and optimal <semantics>Lp</semantics> 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.