The purpose of this paper is to investigate the numerical performances of the hard thresholding procedure introduced by Kerkyacharian and Picard (2004) for the non-parametric regression model with random design. That construction adopts a new approach by using a wavelet basis warped with a function depending on the design, which enables to estimate regression functions under mild assumptions on the design. We compare our numerical properties to those obtained for other constructions based on hard wavelet thresholding. The performances are evaluated on numerous simulated data sets covering a broad variety of settings including known and unknown design density models, and also on real data sets
