数学物理学报(英文版) ›› 1999, Vol. 19 ›› Issue (1): 37-44.

• 论文 • 上一篇    下一篇

RELATIVE STABILITY FOR LOCAL MEDIAN ESTIMATE

 杨瑛   

  1. Department of Probability and Statistics, Peking University, Beijing 100871, China
  • 收稿日期:1996-12-24 修回日期:1997-09-15 出版日期:1999-03-02 发布日期:1999-03-02
  • 基金资助:

    Research Supported by NSFC (Grant No.19871003) and the
    Doctoral Foundation of Education of China.

RELATIVE STABILITY FOR LOCAL MEDIAN ESTIMATE

 YANG Ying   

  1. Department of Probability and Statistics, Peking University, Beijing 100871, China
  • Received:1996-12-24 Revised:1997-09-15 Online:1999-03-02 Published:1999-03-02
  • Supported by:

    Research Supported by NSFC (Grant No.19871003) and the
    Doctoral Foundation of Education of China.

摘要:

Consider the nonparametric median regression model Yni= g(xni) + ?ni, 1 
i  n, where Yni’s are the observations at the fixed design points xni 2 [0, 1], ?ni’s are
independent identically distributed random variables with median zero, g(x) is the smooth
function of interest. Suppose the local median estimate egn,h(x) of g(x) admits the Ba-
hadur’s representation. Under some regular conditions, the relative stability of the local
median estimate is established in the L2 sense.

关键词: Local median estimate, relative stability, nonparametric median regression.

Abstract:

Consider the nonparametric median regression model Yni= g(xni) + ?ni, 1 
i  n, where Yni’s are the observations at the fixed design points xni 2 [0, 1], ?ni’s are
independent identically distributed random variables with median zero, g(x) is the smooth
function of interest. Suppose the local median estimate egn,h(x) of g(x) admits the Ba-
hadur’s representation. Under some regular conditions, the relative stability of the local
median estimate is established in the L2 sense.

Key words: Local median estimate, relative stability, nonparametric median regression.62J

中图分类号: 

  • 62J