Large Deviations for a Test of Symmetry Based on Kernel Density Estimator of Directional Data

摘要

Assume that f_(n)is the nonparametric kernel density estimator of directional data based on a kernel function K and a sequence of independent and identically distributed random variables taking values in d-dimensional unit sphere S^(d-1).We established that the large deviation principle for{sup_(x∈S^(d-1))fn(x)-fn(-x),n≥1}holds if the kernel function is a function with bounded variation,and the density function f of the random variables is continuous and symmetric.