  Needlets have been recognized as state-of-the-art tools to tackle spherical
data, due to their excellent localization properties in both spacial and
frequency domains.
  This paper considers developing kernel methods associated with the needlet
kernel for nonparametric regression problems whose predictor variables are
defined on a sphere. Due to the localization property in the frequency domain,
we prove that the regularization parameter of the kernel ridge regression
associated with the needlet kernel can decrease arbitrarily fast. A natural
consequence is that the regularization term for the kernel ridge regression is
not necessary in the sense of rate optimality. Based on the excellent
localization property in the spacial domain further, we also prove that all the
$l^{q}$ $(01\leq q < \infty)$ kernel regularization estimates associated with
the needlet kernel, including the kernel lasso estimate and the kernel bridge
estimate, possess almost the same generalization capability for a large range
of regularization parameters in the sense of rate optimality.
  This finding tentatively reveals that, if the needlet kernel is utilized,
then the choice of $q$ might not have a strong impact in terms of the
generalization capability in some modeling contexts. From this perspective, $q$
can be arbitrarily specified, or specified merely by other no generalization
criteria like smoothness, computational complexity, sparsity, etc..
