Asymptotic properties of nonparametric M-estimation for mixing functional data

Jia Chen, Li Xin Zhang

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We investigate the asymptotic behavior of a nonparametric M-estimator of a regression function for stationary dependent processes, where the explanatory variables take values in some abstract functional space. Under some regularity conditions, we give the weak and strong consistency of the estimator as well as its asymptotic normality. We also give two examples of functional processes that satisfy the mixing conditions assumed in this paper. Furthermore, a simulated example is presented to examine the finite sample performance of the proposed estimator.
Original languageEnglish
Pages (from-to)533–546
Number of pages14
JournalJournal of Statistical Planning and Inference
Issue number2
Early online date22 May 2008
Publication statusPublished - 1 Feb 2009


  • αα-Mixing
  • Asymptotic normality
  • Consistency
  • Functional data
  • Nonparametric M-estimation

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