  We consider the statistical analysis of random sections of a spin fibre
bundle over the sphere. These may be thought of as random fields that at each
point p in $S^2$ take as a value a curve (e.g. an ellipse) living in the
tangent plane at that point $T_{p}S^2$, rather than a number as in ordinary
situations. The analysis of such fields is strongly motivated by applications,
for instance polarization experiments in Cosmology. To investigate such fields,
spin needlets were recently introduced by Geller and Marinucci (2008) and
Geller et al. (2008). We consider the use of spin needlets for spin angular
power spectrum estimation, in the presence of noise and missing observations,
and we provide Central Limit Theorem results, in the high frequency sense; we
discuss also tests for bias and asymmetries with an asymptotic justification.
