Adaptive Nonparametric Regression on Spin Fiber Bundles
  The construction of adaptive nonparametric procedures by means of wavelet
thresholding techniques is now a classical topic in modern mathematical
statistics. In this paper, we extend this framework to the analysis of
nonparametric regression on sections of spin fiber bundles defined on the
sphere. This can be viewed as a regression problem where the function to be
estimated takes as its values algebraic curves (for instance, ellipses) rather
than scalars, as usual. The problem is motivated by many important
astrophysical applications, concerning for instance the analysis of the weak
gravitational lensing effect, i.e. the distortion effect of gravity on the
images of distant galaxies. We propose a thresholding procedure based upon the
(mixed) spin needlets construction recently advocated by Geller and Marinucci
(2008,2010) and Geller et al. (2008,2009), and we investigate their rates of
convergence and their adaptive properties over spin Besov balls.
