Asymptotic normality of the Lk-error of the Grenander estimator

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We investigate the limit behavior of the Lk-distance between a decreasing density f and its nonparametric maximum likelihood estimator f¿n for k¿1. Due to the inconsistency of f¿n at zero, the case k=2.5 turns out to be a kind of transition point. We extend asymptotic normality of the L1-distance to the Lk-distance for 1¿k1, we show that the Lk-distance between f and f¿n is asymptotically equivalent to the Lk-distance between Un and g. Primary Subjects: 62E20; 62G07 Secondary Subjects: 62G20 Keywords: Brownian motion with quadratic drift; central limit theorem; concave majorant; isotonic estimation; L_k norm; monotone density
Original languageUndefined/Unknown
Pages (from-to)2228-2255
Number of pages28
JournalAnnals of Statistics
Issue number5
Publication statusPublished - 2005


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