Exponential inequalities for dependent V-statistics via random Fourier features

Abstract

We establish exponential inequalities for a class of V-statistics under strong mixing conditions. Our theory is developed via a novel kernel expansion based on random Fourier features and the use of a probabilistic method. This type of expansion is new and useful for handling many notorious classes of kernels.

This is the first part of the arxiv preprint (arXiv:1902.02761), and is to appear in Electronic Journal of Probability (EJP). The second part of the arxiv preprint will be submitted to a statistical journal