基于R^d上核密度估计的对称检验的中偏差

Moderate Deviations and Large Deviations for a Test of Symmetry Based on Kernel Density Estimator in R^d

设f_n是基于一个核函数K和取值于R^d的独立同分布随机变量列的一个非参数核密度估计.推广了何和高一文中相应中偏差的结果,即证明统计量sup_(x∈R)~d|f_n(x)-f_n(-x)|的中偏差,并给出了两个具体的模拟例子.

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^d. The goal of this article is to extend the results of moderate deviations in [4], i.e., to prove moderate deviations for the statistic supx∈R^d｜fn（x）-fn（-x）｜, and moreover present two concrete simulated examples.