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
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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 \leqslant p \lt \infty ) 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。Abstract: 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 \leqslant p \lt \infty ) -consistency in both regular-smooth and super-smooth cases was proved. This conclusion can help researching the convergence rates of wavelet estimator.