On the maxiset comparison between hard and block thresholding methods

Autin [2007. Maxisets for μ-thresholding rules. Test, to appear, see 〈http://www.seio.es/test/Archivos/issues/Ab_TESTAutin.html〉] has established the following estimation result: by considering the Gaussian white noise model and the Besov risk Bp,p0, the BlockShrink estimator is better in the maxiset sense than the hard thresholding estimator. In the present paper, we show that this maxiset superiority is strict and can be extended to the Lp risk for numerous sophisticated models (regression with random uniform design, convolution model in Gaussian white noise,…).