Acta mathematica scientia,Series B ›› 1999, Vol. 19 ›› Issue (1): 37-44.

• Articles • Previous Articles     Next Articles

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.

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

CLC Number: 

  • 62J
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