方向数据核密度估计强一致相合性的收敛速度

Rates of Strong Uniform Consistency for Kernel Density Estimators of Directional Data

设f_n为基于核函数K和一列取值于d维单位球面的独立同分布的随机变量上的非参数核密度估计。该文通过经验过程的方法得到核密度估计强一致相合性的速度。

Let fn be the non-parametric 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. A rate of strong uniform consistency for the kernel density estimators is presented by the empirical process method.