Consistency of wavelet estimator in the multivariate multichannel deconvolution model
To estimate multivariate signals in a class of multichannel deconvolution models,this paper constructs a linear wavelet es-timator by Fourier analysis,weighted summation,and wavelet projection methods.Without assuming the smoothness of unknown signal,that the wavelet estimator satisfies the mean Lp(1 ≤ p＜∞)-consistency in both regular-smooth and super-smooth cases was proved.This conclusion can help researching the convergence rates of wavelet estimator.
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