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

Andrzej S. Kozek*, Mirosław Pawlak

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)


    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 co-incides with the L1-functional and with the conditional median.

    Original languageEnglish
    Pages (from-to)343-353
    Number of pages11
    JournalStatistics and Probability Letters
    Issue number4
    Publication statusPublished - 15 Jul 2002


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