Wavelet threshold estimation of a regression function with random design

  • Authors:

  • Shuanglin Zhang;Man-Yu Wong;Zhongguo Zheng

  • Affiliations:

  • Michigan Technological University/ and Heilongjiang University, Harbin, China;Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China;Peking University, Beijing, China

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2002

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Abstract

The wavelet threshold estimator of a regression function for the random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov Space Bp, qs is proved under general assumptions. The adaptive wavelet threshold estimator with near-optimal convergence rate in a wide range of Besov scale is also constructed.