[1]School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China [2]College of Sciences, Wuhan University of Science and Technology, Wuhan 430081, China
Abstract:
Let fn be a non-parametric kernel density estimator based on a kernel function K. And a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup x∈R|fn(x) - fn(-X)|.