On M-Estimators and normal quantiles

Andrzej S. Kozek*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)
    7 Downloads (Pure)


    This paper explores a class of robust estimators of normal quantiles filling the gap between maximum likelihood estimators and empirical quantiles. Our estimators are linear combinations of M-estimators. Their asymptotic variances can be arbitrarily close to variances of the maximum likelihood estimators. Compared with empirical quantiles, the new estimators offer considerable reduction of variance at near normal probability distributions.

    Original languageEnglish
    Pages (from-to)1170-1185
    Number of pages16
    JournalAnnals of Statistics
    Issue number4
    Publication statusPublished - Aug 2003


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