Acta mathematica scientia,Series B ›› 2000, Vol. 20 ›› Issue (1): 1-11.

• Articles •     Next Articles

ON THE CONSISTENCY OF CROSS-VALIDATION IN NONLINEAR WAVELET REGRESSION ESTIMATION

 ZHANG Shuang-Lin, ZHENG Zhong-Guo   

  1. Department of Probability and Statistics, Beijing University, Beijing 100871, China
  • Online:2000-01-07 Published:2000-01-07
  • Supported by:

    The reseach is supported by Doctoral Programme Foundation, National Natural Science Foundation of China and Natuural Science Function of Heilongjiang Province, China.

Abstract:

For the nonparametric regression model Yni = g(xni) + "nii = 1, · · · , n, with regularly spaced nonrandom design, the authors study the behavior of the nonlinear wavelet estimator of g(x). When the threshold and truncation parameters are chosen by crossvalidation on the everage squared error, strong consistency for the case of dyadic sample size and moment consistency for arbitrary sample size are established under some regular
conditions.

Key words: Consistency, cross-validation, nonparametric regression, threshold, truncation, wavelet estimator

CLC Number: 

  • 62G
Trendmd