一类带加法噪声密度卷积的小波估计

Wavelet Estimation for Convolution of Densities With Additive Noises

摘要: 利用小波方法研究一类带加法噪声密度函数卷积问题，构造密度函数卷积的小波估计器，并给出其在Besov球B_r，q^s（L，M）的L^p平均收敛阶.当r ≥ p=2时，本研究的主要定理可以退回至Chesneau和Navarro（2014）的结论.

Abstract: The estimation for convolution of densities with additive noises by wavelets was discussed in this parer. Wavelet estimator of the convolution of densities was constructed and the upper bounds over L^p risk on Besov balls B_{r, q}^s(L, M) were provided. When r ≥ p=2, our result coincides with Chesneau & Navarro, s (2014) theorem.