Adaptive Density Estimation on the Circle by Nearly-Tight Frames

This paper is focussed on nonparametric density estimation in the framework of circular data. We develop a procedure based on wavelet thresholding methods. In particular, the wavelets used are the so-called Mexican needlets, which represent a nearly-tight frame on the circle and are characterized by a strong localization property in the real space domain. We study the asymptotic behaviour of the $L^{2}$-risk function associated to these estimates and we show that its rate of convergence is nearly optimal.