基于R^d上核密度估计的对称检验的大偏差（英文）

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.本文推广了在He和Gao(2008)中相应大偏差的结果,即证明统计量sup x∈Rd|f_n(x)-f_n(-x)|的大偏差.

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 large deviations results in He and Gao （2008）, i.e., to prove large deviations for the statistic sup x∈R^d｜fn（x）-fn（-x）｜.