数学物理学报 ›› 2009, Vol. 29 ›› Issue (3): 707-715.

• 论文 • 上一篇    下一篇

方向数据核密度估计强一致相合性的收敛速度

  

  1. (武汉大学数学与统计学院 |武汉 430072)
  • 收稿日期:2007-12-30 修回日期:2009-01-07 出版日期:2009-06-25 发布日期:2009-06-25
  • 基金资助:

    国家自然科学基金(10571139)资助

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

  • Received:2007-12-30 Revised:2009-01-07 Online:2009-06-25 Published:2009-06-25
  • Supported by:

    国家自然科学基金(10571139)资助

摘要:

fn 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.

关键词: 核密度估计, 球面数据, 强一致相合性

Abstract:

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  Sd-1. A rate of strong uniform consistency for the kernel density estimators is presented by the empirical process method

Key words: Kernel density estimator, Spherical data, Strong uniform consistency

中图分类号: 

  • 60F10