Refined Large Deviations for von Mises Statistics
Peter Eichelsbacher · Theory of Probability and Its Applications · 2005
We give sufficient conditions for the large deviations principle of real-valued von Mises statistics, improving previous results. As a consequence we obtain sufficient conditions for the large deviations principle for Banach space valued U-statistics, improving previous results as well. The proofs are based on large deviations results for stochastic processes due to Arcones and a spectral decomposition of the kernel function of the von Mises statistic and the U-statistic, respectively.