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Distribution-free consistency of kernel non-parametric M-estimators

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  • Kozek, Andrzej S.
  • Pawlak, Miroslaw

Abstract

We prove that in the case of independent and identically distributed random vectors (Xi,Yi) a class of kernel type M-estimators is universally and strongly consistent for conditional M-functionals. The term universal means that the strong consistency holds for all joint probability distributions of (X,Y). The conditional M-functional minimizes (2.2) for almost every x. In the case M(y)=y the conditional M-functional coincides with the L1-functional and with the conditional median.

Suggested Citation

  • Kozek, Andrzej S. & Pawlak, Miroslaw, 2002. "Distribution-free consistency of kernel non-parametric M-estimators," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 343-353, July.
    • Handle: RePEc:eee:stapro:v:58:y:2002:i:4:p:343-353
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    References listed on IDEAS

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    1. Györfi, László & Walk, Harro, 1997. "On the strong universal consistency of a recursive regression estimate by Pál Révész," Statistics & Probability Letters, Elsevier, vol. 31(3), pages 177-183, January.
    2. Boente, Graciela & Fraiman, Ricardo, 1989. "Robust nonparametric regression estimation," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 180-198, May.
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