1Wavelet Estimation Via Block Thresholding: A Minimax Study Under The Lp Risk

Abstract: We investigate the asymptotic minimax properties of an adaptive wavelet block thresholding estimator under the Lp risk over Besov balls. It can be viewed as a Lp version of the BlockShrink estimator developed by Cai (1996,1997,2002). Firstly, we show that it is (near) optimal for numerous statistical models, including certain inverse problems. Under this statistical context, it achieves better rates of convergence than the hard thresholding estimator introduced by Donoho and John-stone (1995). Secondly, we apply this general result to a deconvolution problem. Key words and phrases Minimax estimation; Lp risk; Besov spaces; wavelets; block thresholding; convolution in Gaussian white noise model