Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (5): 1453-1463.

• Articles • Previous Articles    

Berry-Esseen Bounds for Wavelet Estimator of Regression Function under Strong Mixing Process

  

  1. 1.Department of Mathematics, Shangrao Normal University, |jiangxi Shangrao 334001; 2.School of Mathematical Sciences, Guangxi Teachers Education University, Nanning 530023
  • Received:2008-04-11 Revised:2009-06-10 Online:2009-10-25 Published:2009-10-25

Abstract:

Consider the nonparametric regression model Yni=g(tni)+εni~ (i=1, …, n) with wavelet method, where the design points {tni} are known and nonrandom,  g(?) is an unknown function defined on the closed interval [0,1],  and  {εni} are  strictly stationary strong mixing processes.
 Under appropriate conditions,  we derive Berry-Esseen bounds for wavelet estimator of g(?).  As a corollary, we give the Berry-Esseen bounds that can attain  O(n-1/6).

Key words: Wavelet estimator, Fixed design regression, Strong mixing, Berry-Esseen bound

CLC Number: 

  • 62G05
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