Tail behavior of dependent V-statistics and its applications

Abstract

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.