On Bayesian testimation and its application to wavelet thresholding
贝叶斯检验与估计及其在小波阈值化中的应用
We consider the problem of estimating the unknown response function in the Gaussian white noise model. We first utilize the recently developed Bayesian maximum a posteriori testimation procedure of Abramovich et al. (2007) for recovering an unknown high-dimensional Gaussian mean vector. The existing results for its upper error bounds over various sparse lp-balls are extended to more general cases. We show that, for a properly chosen prior on the number of nonzero entries of…