  This work is concerned with the study of asymptotic properties of
nonparametric density estimates in the framework of circular data. The
estimation procedure here applied is based on wavelet thresholding methods: the
wavelets used are the so-called Mexican needlets, which describe a nearly-tight
frame on the circle. We study the asymptotic behaviour of the $L^{2}$-risk
function for these estimates, in particular its adaptivity, proving that its
rate of convergence is nearly optimal.
