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Asymptotic properties of nonparametric M-estimation for mixing functional data

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Publication details

JournalJournal of Statistical Planning and Inference
DateE-pub ahead of print - 22 May 2008
DatePublished (current) - 1 Feb 2009
Issue number2
Volume139
Number of pages14
Pages (from-to)533–546
Early online date22/05/08
Original languageEnglish

Abstract

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.

    Research areas

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

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