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.

References in corpus (5)

• Exponential and moment inequalities for U-statistics
• Moment inequalities for U-statistics
• Degenerate U- and V-statistics under weak dependence: Asymptotic theory and bootstrap consistency
• Deriving the asymptotic distribution of U- and V-statistics of dependent data using weighted empirical processes
• Inference of weighted $V$-statistics for nonstationary time series and its applications

Cited by in corpus (1)

• Probability inequalities for high dimensional time series under a triangular array framework