Adaptive density estimation on the circle by nearly tight frames

In this work, we study the Lp-risk with p ≥ 1 of nonparametric density estimators by using wavelet method in the framework of circular data. In particular, these estimators are based on local hard thresholding techniques; furthermore, they are constructed over the so-called Mexican needlet system, which describes a nearly tight frame over the circle. We prove that these estimators are adaptive and the rates of convergence for their Lp-risks are optimal in a class of functional spaces, that is, the Besov spaces, also by means of the concentration properties characterizing the Mexican needlets.