Acta mathematica scientia,Series B ›› 2004, Vol. 24 ›› Issue (1): 61-70.

• Articles • Previous Articles     Next Articles

BOOTSTRAP WAVELET IN THE NONPARAMETRIC REGRESSION MODEL WITH WEAKLY DEPENDENT PROCESSES

 LIN Lu, ZHANG Run-Chu   

  • Online:2004-07-13 Published:2004-07-13
  • Supported by:

    This paper is supported by NNSF project (10371059) of
    China and Youth Teacher Foundation of Nankai University.

Abstract:

This paper introduces a method of bootstrap wavelet estimation in a non-
parametric regression model with weakly dependent processes for both fixed and random
designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estima-
tors are given in the fixed design model. The conditional normality for a modified version
of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for
the bootstrap wavelet estimator is also proved in the random design model. These results
show that the bootstrap wavelet method is valid for the model with weakly dependent
processes.

Key words: Nonparametric regression;weakly dependent process;bootstrap;wavelet

CLC Number: 

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