多元多通道反卷积模型中小波估计的相合性  

Consistency of wavelet estimator in the multivariate multichannel deconvolution model

作　　者：郭慧君 李树滋 GUO Huijun;LI Shuzi(School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2024年第1期75-80,共6页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(12001132);广西高等教育本科教学改革工程项目(2021JGA189)。

摘　　要：针对一类多通道反卷积模型中多元信号的估计问题,利用傅里叶分析、加权求和与小波投影方法,构造了线性小波估计器。在不假定未知信号光滑性的条件下,证明了上述小波估计器在普通光滑、超光滑2种情形均满足平均L^(p)(1≤p<∞)相合性。该结论为研究小波估计器的收敛阶提供了理论支持。To estimate multivariate signals in a class of multichannel deconvolution models,this paper constructs a linear wavelet estimator by Fourier analysis,weighted summation,and wavelet projection methods.Without assuming the smoothness of unknown signal,that the wavelet estimator satisfies the mean L^(p)(1≤p<∞)-consistency in both regular-smooth and super-smooth cases was proved.This conclusion can help researching the convergence rates of wavelet estimator.

关 键 词：小波 反卷积 相合性 傅里叶分析 布朗单 

分 类 号：O174.2[理学—数学]