  We establish exponential inequalities and Cramer-type moderate deviation
theorems for a class of V-statistics under strong mixing conditions. Our theory
is developed via kernel expansion based on random Fourier features. This type
of expansion is new and useful for handling many notorious classes of kernels.
While the developed theory has a number of applications, we apply it to
lasso-type semiparametric regression estimation and high-dimensional multiple
hypothesis testing.
