基于偏差密度的各向异性小波估计  

Anisotropic wavelet estimation based on biased density

作　　者：朱亚玲 许俊莲 ZHU Ya-ling;XU Jun-lian(School of Mathematics and Information Science,Baoji University of Arts and Sciences,Baoji 721013,Shaanxi,China)

机构地区：[1]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《宝鸡文理学院学报(自然科学版)》2025年第1期1-5,共5页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：国家自然科学基金青年资助项目(12101014);宝鸡文理学院校级研究生创新项目(YJSCX24YB37)。

摘　　要：目的基于乘法噪声模型,估计各向异性非紧支密度函数。方法利用各向异性Besov空间的定义及其小波刻画、Jensen不等式和Rosenthal不等式给出相关辅助结论以及主要定理的证明过程。结果构造出来的各向异性线性小波估计器可以达到最优估计,并且与各向同性小波密度估计结果一致。结论将无噪声模型下的结论推广到了乘法噪声模型上,更具有理论意义和现实意义。Purposes—To estimate anisotropic un-compactly supported density function d based on the biased density model.Methods—The definition of anisotropic Besov space and its wavelet characterization,Jensen's inequality and Rosenthal's inequality are used to prove the relevant auxiliary conclusions and the main theorem.Results—The anisotropic linear wavelet estimator can achieve the optimal estimation,and the results are consistent with the isotropic wavelet density estimation.Conclusions—It is of theoretical and practical significance to generalize the conclusions of the noise-free model to the multiplicative noise model.

关 键 词：偏差密度 小波估计器 各向异性 BESOV空间 L^(p)风险 

分 类 号：O174.2[理学—数学]