Abstract:

Let f_n 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\limits_{x\in{{\Bbb R}}}| {f_{n}(x)-f_{n}(-x)}| $.

Key words: Symmetry test, kernel estimator, moderate deviations, large deviations