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

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.